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String Theory and MTheory  Lecture 10
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a Stecher University my
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Wheeler talking about something called T do our he'd allowing was very very important the history of the mathematical development of string theory but the back over again and discuss more fully and there were tell plenty you of how it led to the concept of beat brings there have been brains have become something of a mathematical pulled off a stunning quantum field theories that kind of quantum field theories but another the gravity another kind of quantum field theories that we use the daytoday basis to understand a choir the dynamics and even quantum field theories that are interesting the it we won't get of this obviously we won't get us today but just try to give you some armed picture of what it's about but we we imagined it was some compact directions are compact more ones which rolled up the simplicity I will imagine that the compact education is toroidal on chloride In other words I'm not necessarily dimensional chorus or onedimensional choruses a circle or interval with the points being identified by twodimensional forests is they are erect a parallelogram doesn't have to be a state parallelogram with opposite sides identified on a threedimensional forests is Cuomo not necessarily a cube but a prototype Thank you parallelopiped up with opposite faces identified the point and that point the point at that point and your from back our in general and any day mentioned the concept of a forest there you go welldefined concept and those are the easiest cases but those are the easiest of the study In these cases of course supplement on top of this Is the ordinary 4 dimensions of space time so this is what present at every point of space time when there is based current below other directions that we can more somebody small enough move and send them back to set up now let's focus on 1 particular place waste time and ask what could be a particle could be there but now that's zeroing in on zoom in and guess what that particle looks like on scales which are so small but these compact directions become visible so let's start with a simple picture that we had just 2 were just to get started we imagine the 1 large direction In 1 small direction the small direction now would be called a circle the circle not be caused it's embedded in 2 dimensions of the circle but just because it's Haiti to detail that a new around comeback Commack and place so that's our space time waste time on time is it time into it time is not draw Mumbai is pure space In this case twodimensional but I feel like we can generalize time dimensions Compaq directions become tore the month compact directions of the big ones just become are threedimensional space so however many dimensions as now are constrained theory particles are strings let's take the case of mostly series of the same different from each other but this a fairly small classification of them the string theories that I'm interested in right now have only closed strength would come back to what happens when you open strings wild but for the moment only closed string no that's No. 1 so I probably like rubber bands they are closed and furthermore that what we would call we call oriented oriented means that was it intrinsic this difference between going around the string in 1 direction rather than the other direction it's mathematically like a rubber band in which on the rubber band to a series of arrows to indicate direction there will keep track of orientation the example of what that orientation would say is when the strings bled works like this that was Split entered tool strings with the same orientation on the block or so in that sense orientation preserved for strings they remembered center which now that doesn't mean that they're in equivalent community there may be a symmetry and the sense that a string with the opposite orientation may have all the same properties but what it does mean is it you conclude pair 2 strings to see whether they have the same orientation or the opposite orientation brick Semel electric charge Our positive electric charges behave exactly the same way as negative of electric charges in In that for example if you replaced in the real world and electron by a positron every Proton by any of that and with it every neutron by charm chemistry would remain exactly the same partly storm very very high precision would remain on changed so in that sense plus charges are identical to minus charges but you can't tell the difference between the putt that no you can't tell them between the plus Georgia minister of 2 charges you could tell whether they are the same or office how pursue a very
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attractive rip you can't tell where both plus or minus but you can't tell OK so so say this true of oriented she rings that they have a sense of orientation if you replaced every strain in string theory by a string of the opposite orientation theory would be the same but if you have 2 strings you could tell the same orientation are out of work just call oriented that it could wrap them what you could do 2 things you can have a strain which is not 1 around the Come ache some compact direction there it is the drawn on the surface of the twodimensional world here its freedom moved it can move in this direction or can move realm so it can have momentum and that momentum could be along the direction of the larger directions or it can be along the shore what can be a combination of both they can I it has momentum we could think of that as motion and the control of this way Kabul this way or even lower than a year In a killer pattern like that having both component to momentum on the among the components of the momentum in the short directions the finite compact corrections are quite yeah quantized in integer multiples of D in numerous radius in Mercer conference the distance around the closed the quarter cycle is here all later the still the relates to miss won't normally is around a toe to allay a later 0 Bhutto Pfeffer who knew what space mom Mom this is not said Matt this is some X this could be X callers direction y around here that's they said real space similar adjuster parameter of which changes along the string of bitches meaning the points along with growing your rubber band a rubber band is composed of molecules molecules convening the 1st molecules Harry enjoyed Fred and Sara and so forth that's it meaning the particles as you around the strength but a string is closed and because that what was was done we have a direction that is place look on it not bomb Joel with was not but Will Comparex OK show Segner various along here along the strain because some 0 2 pipe but that has nothing whatever to do with the stringers wrapped around space so think of I'm sorry legal rubber band they band work on the surface of the rubber band marked off Sydney equals zeroes in Naples a small number of twice the small number as we go around the rubber rubber band I would mark a points on rubber band that's said that's it has nothing to to do with whether I wrapped the rubber band around my wrist or not it's always there stigma goes around wants as as the angle as we follow the string around the song shape goes from 0 to to it's a completely separate question of whether the strain is wrap overwhelmed the extra dimension and the same sense that a rubber band could be wrapped around rich you could wrap the rubber band around you is the only in rubber band Ucon rapid so bad arrows point this way or facility arrows point this way so we have 2 kinds of rap strain it wrapped the correct terms while while around a compact direction years Warner that comes around the other side and the points that way that's warned the other 1 hose the opposite direction let's take talk 1 ounce strings like thorns things like this we just drove differently but for but this way this 1 goes but what can happen to toward strings which warned in opposite directions well remember the basic based on process of string theory is strings to come together and join display virologist but when they joins orientation was remembered a string like this and the string like this can put some more orientation arrows on but says Calicut Jory they can join where that I don't think I need words to describe it I think the picture describes it well enough the have to be horrible arrows have to be continuous would you can't have it is a strained splitting somehow like that try you know why can't be continuous you rental contradiction Aziz . com together 5 so this is the kind of thing that can happen the opposite namely time reversal of it can also happened streams which I like this can come together and join soulful 5 at the basic phenomena of splitting in joining and thing which is governed by coupling constant so what can happen he ate Raptors clear this compact but still I lost track of your reorientation now it's not really well anymore as from the point of view of topology you care allowing it into this always done years we've taken this week stretched around and join the Forest Side performed the original 1 pair well we cannot do that and now it's on wild it's just a a single on warm spring I that 1 way to think about it is to keep track of winding number winding number can be defined to be positive for windings which look this way will call at winding number 1 overwhelmed the other way will call winding number might try to give you a mathematical definition winding my race if arrows point this way will call positive warning effect for the other way will call may get worry if I have a single strain which is why like what's the winding winding number is a plus 1 that I have another 1 forget this 1 moment of side with another 1 which is why am this way that has winding number like this 1 the tone together altogether have warned numbers 0 this is winding number 0 it's not worth the ran the so what's reserve it is winding number let's take another case let's imagine now to strings which the same way if wished 2 0 strings warm what can happen to them they have winding number to some of the 2 of them have warning number 2 what can happen well served with over here again Our is going this way
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and become around here said both got the same way you can't unwind you can do something you can have a process of splitting in joining which does this which interconnects them Norway see would Of course demerits With across them but still after they crossed the arrows still continuous is no contradiction in the direction of the arrows this also has winding number to rise 1 strain with winding number 2 this is due strings each 1 was winding number 1 neutron winding number 1 but the sum total of the winding numbers to Elazig another example winding number is concerned you can't change the winding number although you can see the number of connected components have won them over a hundred you could have 1 strain 1 around a hundred times you have to strings each wore the same way 50 times you could have a hundred strings each 1 wants and they can also communicate in the sense that you could morph from 1 configuration others but you can't change the way Hawaii number is absolutely conserved quantities in this kind of string theory never could change let's let's forget why Camilla combat a winding numbered among all that we should discuss warned me on this 1 over here packages be thought of as I knew particle watchers think of as little particle it's a string but part what's a characterized by its characterized by components of moment characters but many things shape and all sorts of things but in particular let's characterized by its components of momentum and particularly component the momentum in the army and be misdirection over here pick out wool look component momentum and that their action has to be in number of in it didn't number of quantum of momentum and the quantum of momentum has to do with the circumference such as caught the radius around here are distance around your call are the circumference strictly but the on our whose authority is the standard term for it on Lee quantum of momentum and misdirection and also incidentally the quantum of energy in that direction from man is a mess was it is a mess was particles energy momentum a proportional to each other for example grad upon time will in this way this way be energy it is also a berm has also quantized in that unit and sorrow energy of a momentum Is momentum can have either side could be plus a minus the moment momentum energy is always for the same amount in over it has momentum in or are in the hands and energy also an old car that CEO of these on that energy the doodle momentum and in particular moment them along the small direction it's quantized so let's say that on 1 particles and the contribution of energy Duda moment let's think about what they are Yao was the momentum on a string moving in space basically it's just the velocity of the center of mass which at the velocity of the just like a rubber band just like a rubber band momentum Is it a mail density which was simplicity we could take B 1 hour times a man's widow victory 1 for a rubber band kind the velocity solo they velocity the momentum is proportional velocity and we can think of this as D X beat how town is time variable that describes the motion of the strain in the quantum in a simple quantum mechanics of described previously there's gotta be integer multiples now let's think about the wellknown strings the strings which away from the was a typical energy of a while stirring well strings a certain tension let's just go work in units in which that pensioners 1 but tension is energy per unit Lane so for energy per unit length of is giving a GPO acclaimed then energy of all strain is not in divided by all are but some other integer recall the other integer W W stands for winding number times the energy of a collection of strings which I 1 around here are the integer winding number Carter whereas b energy of a string which is not formed around compact direction is a divided by so I think we talk about this last time but let's discuss again a little bit but suppose that Aura's very small Healy have the specter of the strings which are not 1 of the separation between the levels is a large large because while Boras large so it looks like this where the separation being of order 1 OR and equals 0 fears In equals 1 so for now let's look at the spectrum of the wellknown strings of aridity energy levels of a while those are also In integer multiples 0 winding number 1 winding number 2 widening minus 1 warning them of tool for now W. Hinds Our so that means if waters large where SARS wanderers more beers are were small mistake Mr. Norris largest more are small OK so that makes a separation large Kia Motor makes very small here not got to the other extreme another we talked about this before but I wanna reiterated again let's go to the other extreme this is all lips less then some unit of late in string theory the natural you move linked string theory which is caught 1 hears are much bigger than 1 what are the energy levels or quite well far much bigger than 1 1 0 Morris small and these expectations here we are very close together for obvious are is very large so takes a large energy to wrap around this surpass bullion new Liu could measure about these particles namely the things assault on talking repertories associated with the compact direction the only thing that you can measure about the compact directions but suppose was the energy of the particles and you're trying to figure out what the radius of compact application of snow was a radius of compact education was the radius of compact application well your problem is how do you tell the difference between particles which have energy with respect to the compact correction because they have momentum or because they have winding number it can't obviously just the energy levels you can't tell solve With this particular spectrum is
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an ambiguity are you In the theory with a small compact education in which large separations between different meant that small separation between different winding number or are you a world with a very large radius of compact provocation and which the role of winding number and momentum change you think well maybe the daughter of a kind of experiments maybe could scatter these particles together seaward comes off 1 of these very very remarkable mathematical facts about string theory is that the inability to tell which kind of world you're in it is rigorously correct Everything that you can calculate about string collisions between them that that 2 different theories with a very different way ATI of compact vacation if you'll interchange winding up with them with but scholar with momentum around compact correction the theories behave in exactly the same way conclusion are in a cinch it doesn't make sense to think of the compact pickup vacationers smaller than the size of a certain size with a cross over interchange and the size of compact vacations smaller than that adjust entirely equivalent for larger compact vacation with our our winding with a 1st is at this 1 you well an saying it it says that there is a cemetery at some of the symmetry and Armed with physicist used the term rally which means an equivalent between different descriptions of his desire of interest for the 1st time in some units are equally warm there you have some extra special symmetry that you were there not only can you tell which have fear urine but you can't tell which is which I which are and yet there is a special point now I wrote an equation over here that armed momentum is equal to DXT now make that a little more precise every point on the strain has a motion in particular and thinking about the motion around the compact correction but different parts of the string could couldn't principal removing different than other parts of the string America be differentially moving in different directions from different speeds so what the former made them that we're talking about a coverup momentum is actually the sum of the moment of all the little bits of it is the summer delayed figure was an in the over the entire string of the velocity XT Kowloon which excimer talking about I'm talking about why actually when that goes around string 1 what about the winding number but we may have a mathematical expression for of winding number momentum there'll be stream which is 1 of the simplest possibility it's while under and he this is a Y coordinate the white worn is periodically comes back to itself but this trend also has a similar coordinates the strain also has a signal coordinate and that's embedded in a string if the string of his very simple way another way of saying it Is that segment is proportional Hawaii actually wiII divided by the total radius of compact education why comes back with self after going aura and signal comes back to itself the Lauren around 1 the right relationship is that stigma is why all art system of way of saying that as you go around Sigma as you around the rubber band the world and bows around the White direction when I would guess let's look at these Sigma by that's just where are we similar by BYT adjusted to number would be wise be sealed might be why is proportional to the little spacing between hearing and local winding number is this summer a little bit of this it would be wise as you go around the ring there was the winding number use right times this and the winding number I believe is what I have emigrated with go um White Over are it is equal the same lack of these did not BY is 1 of our His won lot the couple winding number is 1 Omaha in the world BY by July but he said but it makes sense that global warming them away integral a derivative 5th a death which is duo derivative Nevada cases does . 0 everything comes back to itself around but wine doesn't go comeback its sovereignty will raise around why itself changes by into will be white said adjusted Pope will number of times string wraps around that direction so this is kind of curious he duality is funny duality between winding number firm is equivalent to changing NW into changing Oregon 1 are and in the changing BYD how you will I be plenty of America lower construction but keep that in mind that feed duality is the changing winding in momentum into changing aura would 1 of our men in the changing the derivative of white squares the position of the string UYD how would you why baby said no way young you are by how would you are going to be delivered partial port pretty abstract but this is an exact symmetry of string theory you make changes if it's a it's a the secretary is CYD sloppy DYB swap UYV town for 1 reason I introduced who's will White and in half W. this by telling you now because of a toe toe you interchange where were you saw the expression BY baby how you replaced by the expression might be 1 it's a weird thing to do but in all observable quantities scattering amplitudes energy level all the properties of the string theory don't change if you make those changes but but not like what it sees what we
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don't want what it is said that he thought it was somebody make it this spring with you with some energy Hinduism energy among other things may stretch it out for the fact that may stretch out the required theirs but New blast it with a lot of energy and join a very neat configuration over here of course but I blasted away a lot of energy it might be much more complicated than that but still have this kind of configuration now what you've done that and you take into account that the strings would join the Liscum separated itself In the 2 strings with opposite winding number once you've created 2 strings lapis a winding number no longer connected bacon separate from each other bigger separated from each other when they separated from each other well you've got an isolated spring warning No. 1 and another 1 and you just send off palpitant durian never see it again the answer is that in general you cannot prevent it from happening you may have been particularly if the distance around here was large depicts a large amount of energy the movie's winding strings here this year well the energy the energy itself with proportional are for winding number so with a small amount of energy it's not gonna happen there are enough energy to stretch the string that far but if you call like to things with a large amount of energy they Blatter all over the place they stretch out while the chaotic directions and there's some probability that the we connect it will not change the winding member but it will take a single string or perhaps 2 strings which I'm not which collided with each other and convert out of them something with 2 strings of opposite winding number once that happens they separated the go off answer is generally that that will happen collisions if you don't have that would begin with same question Carissa electric charges if you start with a neutral world while their electron well even if they want electrons to gotta something of nothing is nothing but maybe it is done with 4 times you take some photons you collide in together and what comes out as electrons and positrons you take the positrons in you throw them away from away with you push him some distant place your left lecturer that's all sold you you can't have you can't beat you can't forbid them and eventually you will create now and is winding numbers and his mom and that His momentum quantum numbers is quantize momentum when not only in some sense similar to electric charge but they have all of the properties of electric charge them particularly those strings of opposite momentum 1 going around God do this with plea for yet another who's been going around the With respect the big dimensions of space they are those strains these have the same know this December said 1 member OK that's easy but that's because things are the same winding number we repelled 21 moment strings with opposite winding number will attract was this attraction and repulsion this attraction and repulsion actually corresponds to be gravitational attraction repulsion of the higher dimensional theory if we live and a world of that's a threedimensional 3 space dimensions now we had in 1 what kind of their actions then strings which are opposite maybe in different places In the big dimensions different places in the space of a string wrap this way with a string rap that way belt track each other they opposite warned me number tractor each other in our ordinary threedimensional sent likewise if they have they are beyond the same winding number they will repel each other so they led electrical charges on what come along with us electrical repulsive attraction come from comes from electromagnetic field request electromagnetic fields is deeply connected with photons so what as attraction come from the me answer is it condoms From a gravitational but not gravitation in the fourdimensional stands but gravitation in the final image from the extra dimensional and theory extra dimensions the Einstein gravity the extra dimensions manifests itself in the phenomenon of attraction between like moment not cost about attraction between opposite moment in a compact attraction and repulsion of things with the same moment that's not obviously is UCF told you this before it's not that expect some room for the 1st time and in fact Buchanan related to Einstein's field equations let what's not doing our related Einstein's field equations and depth I'm just going to discuss the origin of the electromagnetic field for the analog electromagnetic field associated with this electrical tight behavior of these particles there must be be something like an electric field must be something like a magnetic field of the behaving so much like electrically charged particles but what is it OK so 1st just ordinary Maxwell equations electric and magnetic fields are describable in terms of a vector potential fourdimensional vector potential a new buildup be magnetic field as the curl Of the vector potential and be electric field was related to the time derivative of of the vector potential that's a has 4 compartments let's go over the gravity and 5 dimensions gravity is described by a metric can't share the metric tensor G them and 1 my I use Nuuanu Hang on saving you window for the 4th dimension of ordinary space when they're talking about 5 dimensional world so let's use for the fundamental world and but were eliminated run over they run all that it would merely dimensions all over ordinary space plus 1 1 direction of silicon right we named as having various components genial you know that ordinary dimensions when they GE New 5 is 5 is the 5th extra dimension and then or else G 5 5 those the components RV gravitational field what about what about G 5 new G. New 5 Liberty by New it's metric and the same thing the babies be independent components Of the gravitational field In inside dimensions while this 1 he yeah that's just the metric of fourdimensional space which is the usual Einstein's gravitational field nothing new there hailing have something warehouse the index it has any finding next year but the fight and that is hidden direction we can't see it but also has a new index which means that's a 4th sector we would mistake this subject for a 4 electorate has 4 components is like a meal would make that identification because
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that that is the correct identification nor about G 5 5 that had no matter how no components in the usual fourdimensional spent so it must be a stay that's gala is usually called called the bill upon sometimes called Millicom almost always called fight was G 5 fired its component of the leopard around the direction it tells you how big the 5th direction a G 5 5 is being just a metric of this square of the distance around the 5th corrections when there's a G firefighters being the 1st direction as Big G 5 times more of directions small the metric tensor in 5 dimensions is a field they can vary from place to place all of these things can vary from place to place this is the usual gravitational field vary from place to place this becomes a lawyer catalog of electromagnetic field which can vary from place to place in the scalar which vary from place but wasn't scalar that's gala is the size of a fist direction secondary from place to place somebody asked me that before a newcomer Madam waves and bag where waves the space on not waves of electromagnetism them out with the gravity waves of varying sizes for the 5th the mansion OK but nevertheless quiesce an ordinary vacuum doesn't have such ways it's fixed but in general the size vary from place to place OK this is an electromagnetic field this is an electromagnetic field then it's a it's also a gravitational field and it's an analog electromagnetic field as a gravitational field while other sources of gravitational field that things like energy and momentum in particular the sources of unmixed components of a field like this components of momentum so the source of this component of the gravitational field is actually the momentum in the direction of full of momentum in the direction that means that we source on this analog of vector potential is going to be the component the momentum going around the 5th Correction lesson the momentum quantum numbers the 1 where is the momentum quantum number over here can be thought of as electric charge and all its Ferdinand and includes a client theory in which the new 5 component of the gravitational field is electromagnetic electric charge lament the electric field our component of the may well but but easy that was it that was easy what about and of course further now we can say that um that be elected that electric field is associated with the Grant the rabbit OK now let's come through me 1 number subservience Dean did force no no it is not it isn't a jerk is related are the TrueType are not quantized related to the size of that mention Franken vary from place to place continuous going smoothly code Bilic arm and we feel that the string theory was right to exist in some form or another but many cases mathematics of retreat but come the winding number now I tell you that the winding number also behaves with this property that opposite warning numbers of track Our like winding numbers help they also behave like electric charges but not this scene what kind of electric charge as the momentum quantum numbers it's and if it would 2 kinds of electric fields to kind of electromagnet magnet living side by side too kinds of photons the kinds of charges winding number associated with something we could call winding photons mend our momentum quantum number associated with momentum photons but momentum photons I'm just a piece of the gravitational field of awards the grab at times which polarized along the new 5 direction so what the field was the field while analog a folk art which is he admitted and absorbed by winding number not a moment of our morning number and healing all the answer we have to go back several lectures fairly early lectures but let me remind you this is probably something you've forgotten I told you but I don't think I stressed very hard Let's go back for the spectrum of closed during the closed rings what kind of state other of close ranks look we start with the closed string being totally unexcited oily do we have signed oscillations with excite oscillations with the creation and annihilation operators which create and Excite waves on the strength and inequities annihilation operators particles of creation and annihilation operators waves moving along with is closed strings and just remind you what kind of operated on the ah creation and annihilation operators I won't are just think about creation operators and I will put a little plus because warned the put too many in the a creates a unit of expectations what labels but 1st of all week aides are labeled by directions of space directions is based perpendicular to the momentum of the object of the string of labeled by directions of space but scores all right bye I and equal if the street is going down zaxis X committees why X 1 X tool or can be a Compaq direction so I Heinz very all the their actions space including the ones which are wrapped up as 1 thing they know what the other index that depends on the frequency of the oscillator and that was an integer and tells you how much energy you when you create worries oscillation creates and energy proportional right so In a related frequency i.e. is related directions base and 1 more thing memorial was foreclosed strength Rick whether the way the propagating around the string strings orientated several hours with the wave is going 1 way around the string or the other way around I don't remember anybody remember how we label to lesser scores last mowing waves and right mulling ways a R & and left and right here purely symbolic they refer to the election on a string not left to right real space OK now was a role I told you the rule like all that level matching its own rule on that going to go into the role now I think I explained little bit what have do with but that they had some and the rule is the amount of energy and left the room moving waves must equal the amount of energy in right away that's a fundamental rule of string theory mathematics Prost a hell of a hand that due to violate it but let's see what kind of states we have them 1st of all have the state with no energy unit all that's a pack yard it's not there in superstring theory but
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simple origins of string theory has minus tool units of energy we work that out minus 2 units of energy as a pack and bad things don't worry what's the 1st excite patient what the next energy up well the next energy up is to hit it With the lowest frequency radar to excite 1 unit of energy With an equals war so for example the could hit it with a committee any 1 of the directions space 1 the lowest left all our
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81 ii right but neither of these states over a legitimate option and the reason is because this 1 has 1 year left moving energy and no units of right moving energy this 1 has won you the right moving in Aegean no units of were moving energy so it doesn't satisfy the principle that the amount of energy in left and right have about the pace of these a gun back what's the next thing out the next thing up it is true applied tool units Of the lowest isolated 1 left and 1 right to make sure that you have balanced energy going in the the right and that means a EIA 1 left behind J 1 right eye NJR direction the space of going to a directions of space for simplicity let's imagine the directions a space are the usual 3 directions based plus 1 more namely the 5th direction the thing that I called White 1 1 directions but the 1 and we applied this of course director these are the things we identified with gravity and other massless particles our with polarization that have to do with while there's something new newly when we end this this direction 1 or both of these indices can now be in the direction earlier before we discuss the direction my injury could only be ordinary directions based in these corresponded to grab a times which have polarization light photons polarization of the polarization is characterized by who directions but now I have something new we can have I been ordinary direction and this 1 being the 1st direction of space internal direction small direction for now we have something which has a vector Index the 1st direction here we don't even call out directions based normally so has the same kind of index structure photon would have this is like a photon it has a polarization to moving down zaxis Mr. polarize either XOY your however that many many dimensions we have to worry about and this is very similar but not done now but they like 2 ways to do it you could have this 1 being left them from being right or you can have a on May 1 right a 1 foray the left or the right to possibilities now and it seems like that means but they were up to kinds of particles that behave like photo remove the the correct thing to do would to they had them and subtract them in the sense of quantum mechanics of linear superposition but whether it was big 2 types of objects which have b index structure of photons complete tool kinds of photon fields the the song that's identified with ordinary grab upon moving them the other 1 is identified with another field a separate field that also heroes a structured similar photon and guess what it is connected with it is the field electromagnetic like field whose sources or what winding number sold 1 million combinations associated with momentum and 1 linear combinations associated with the wine list of things 1 of them is associated with Gravitt can't which is which are the field quanta of the gravitational field and the other 1 is associated with something called being you knew which is different than the gravity on different properties but also news rise it's mixed component is also like a folk itself is all we can say now what is see duality and this is a field a field which exist In string theory called Ramon the column Ramon field important works called it is we're just true car is stolen although the women all babies polarized light photons is 1 more nobody has about where about 85 5 a fire a fire left right it that was the 1 that behaves like a scalar that's the 1 associated whose field quanta a field quanta of this 1 over here namely a radius of the year the euro compact off him which is at its worst 1st the plus sign corresponds the momentum and that's the 1 that's associated with gravity on the 1 with the minus sign is associated with the winding number yeah OK so now now we have a more complete idea about duality involves momentum being interchange with winding number it involves all being interchange while are it involves replacing the X these stigma with VX by Botero misses the integral of this the winding number the into of this momentum and finally it involves into changing Jean you'll 5 B 5 still be serious have most of our of course not clear that the ordinary world does have such field we don't know of real particle candidates for all these fields with so at the moment mathematical construction and were explored mathematical construction with lots of ideas about how you lose these these construction bars are the moment every which should exploration of the mathematics of period is plenty of room and these objects into the bridge but I want to get in the from around but civilian that's what he do our after 5 minutes will come back and talk about C duality for open strings and how it leads to a new concept completely new concept core will be brain but sticker break from
1:03:15
now OK so we figured out work to do is very strange interchange of began the big compact geometries with more ones In various bring aren't I wanna concentrate now on the aspect of key duality that has to live below the waist black that is what but now you see the current gymnastics grow from the abductions the people of me over the years is the key duality is more members the implicit mathematics there many of them are very surprising talk about d brains and how 1 was forced cabbies these new objects in theory which are called be brains these from bearish allayed bearish Lay had nothing to to do with them the dead many hundreds of years they should be called P brains Koltchinskii pea brain was ready use Our brain this go beyond AT & T Mike membrane and 1 speaks of D & membrane these days the garish light enough for the dimensions face gave ass stands for the dimensionality of the Bering Strait is a 1 a membrane as a tool brain a solid threedimensional Chung which may be embedded in higher dimensions but solid is brain himself for his deeds a brain where they come from what they do what's there were there not just meet up things they were essential to the consistency of the theory the mathematics absolutely demanded them and the result of knowing about them has been derived and enormous number of equivalent between different theories and fact it turned out that those enormous numbers of equivalents has turned out to be enormous numbers of equivalence between different kinds of geometric structure call answers which the mathematicians had no idea existed between different their call RBI manifolds and which the mathematicians were Kiraly surprised by and it turned out to be confirmed them but this is summer this is now part of the gymnastics string theory and be brains of greater enormously powerful role also the application so let's talk about open strings now be brains have to do with open strings open strings what's the winding number of an open string things don't have stable winding members 5 if have an open strain Compaq space now that this picture it is a shorthand for all of the compact their actions would of which there are presumably sects in superstring theory and all of these opened on compact fiber let's imagine now that an additional tool Close strain open open strings now have hidden points we can't classified and with winding number it doesn't make sense to classify them with winding number not 1 so we have to however we have the thing about what happens to them when we do this process of Treaty duality duality was a phenomena discovered in close strength theory but surprisingly it also makes open string theory on which I would say said something rather remarkable something which is confirmed the other ways but but with think about it on this is straining an open string the rules for open strings to remember what the rules are ah for goes on a peak in the open string boundary conditions on me in the open the remand order and that open strings should satisfy the X would wiII again this is why is X any of accord but let's where particular while that's right from them both the expo ID Sedna equals 0 BY IDC but but what is that correspond to to that corresponds to the idea end of the string is a string it's made up of a lot of trainee infinitesimal mass pouring and supposing the end of the string some stretching PX baby signal was about equal 0 that would exert a force on the very last molecule well as you subdivide the molecules into smaller and smaller structures to build their continuous limit of the string the molecules get wider and wider and wider how much force could you plug mess on the a thing of arbitrarily small man without having it accelerate and the acceleration into 0 and and that means that the string cannot afford that have any net stretching at the end of that that's why that's where these conditions come from the expertise would my babies should be equal 0 and that's the infinite acceleration either in the x direction of a wide array of course there is another possibility in that somebody's holding the end of the string in applying an enormous force To keep from removing but nobody's Stanley holding me in the strain then it is any net tensions in the string you accelerate there are infinitely got to worm basically to remove that structure OK now whereabouts Tito our let's suppose now this a small compact direction we want to replace the hero very very much smaller extremely small who say later that this is supposed to be equivalent to a theory with launch compact direction launch compact enormously large could be cosmological large what I do with open string supposed to replace winding number momentum but remember that momentum was what was rumored the related to was related to X by D. Powell right what was winding number related to the X Buddy Stigler namely exactly what goes on here
1:10:56
I should actually right since our mostly interested in the compact directions for the moment let's concentrate on the Compaq direction Tito hourly and walls of among other things replacing every place you see BY by but yet what do Sigma IDY by house what does it say then about open strings opens hearings when you replace where when they undergo this process of out with you have to do as you have that change the boundary conditions and the boundary conditions at the end of the string become the expiry D. Powell equals 0 forums case arm when that sorry the Seidel hourly is associated with the compact erection we don't want that only the compact directions of being interchanged Smallwood large when not delay all would be on compact 1 compact direction y goes White radius in white direction becomes base Rod Royal was we we were supposed to replace BY babies but hey what might be if strings originally moving on the surface I had no amount boundary conditions BY but was asked if he do they have Dirichlet boundary condition wasn't mean to say that BY power is equal to 0 always trade only at the end points Mississippi ends of the strength it means the end points of forbidden from all over so wherever they started their stopgap the where are they start this not something holding them there it means that this theory has which can nail down the ends of strings are strings there must be 50 duality is to make sense there must be objects in the theory which can nail down millions of strength you start with a theory with no such objects and the strings just move freely and after tea duality you discover some kind of object in the theory which has nailed down the location of the strain its nailed down only the white component we have not played around with the exit the exorcist freedom move compact direction he is now nailed down so where is it nailed down but so based its nailed down someplace someplace and white wine goes around his right off the bat place right over here the something he which is capable of holding ends of strings nailing down that object is called a D brain beef and bearish Larry and it was put in by hand instead were asked what if they're open strings in the theory and the theory has Tito which must have a reason for her by now where road then what happens the open strings when you interchange the small compact direction for large compact correction and the answer is did you discover something new you discover some new kind of object on our rich holders of fewer than half or less what the same is not Korea figure rescue workers can bang With at a joint survey but that young Yao Yao could better but the simplest cases where a gorgeous effects fixed some some position now what position can you put back here here he won't be answered Betty better be able put it anywhere so therefore this has to be a movable object because this is nothing special about 1 point space in the points race wrong that sees his got br movable object which functions as 8 anchor point for the ends strength and its mobile thing you commit what quite sure that it's also bendable Our relativity can make sense were absolutely rigid objects and so will also be bendable but let's just not bend the the moment then strings can attach themselves to it brings a had to it can exist a strain can come on let's look so good at that musical debate is depressed toll surpassing weak talk with lipstick example suppose supposedly we took can Mitchell string theory which has 9 dimensions of space 9 dimensions of space and we made 1 of the compact and then introduced a B brain this way what would be the dimensionality of the it will be 1 9 No 8 8 we came down 1 direction and let be other not the other directions space freedom move around right here is a tabletop that table toppers twodimensional this is an object at tracks the table top commonly directions freedom will be in harmony is a constraint it's freedom open to such is a string of the string widow and my fingers and strengthen its freedom movement to direction and constrained in its 3rd direction so constrained onedimensional a constraint onedimensional it creates a mean threedimensional space 8 tool dimensional surfaced supposedly now in 9 dimensions of space and I constrain the end of a string constrain 1 of the dimensions it becomes at dimensional surface restrained Kimura now I suppose it was no isn't for only constraining window the same thing with any number of compact direction as you can play this see duality game with any subset of the compact direction play that's interesting game and you could be in the same way construct being brains which came down any number Of accord the end of a string commode price a let's take threedimensional space again let's suppose now we play this game and we've constrain the vertical position by doing this he do our trip with respect to the vertical direction supposing I also do it now with respect to from the back correction I constrained motion of the position of the strings constrained vertically and this way that means that the end of the strain pressed move or longer leader the
1:19:12
intersection of this plane without playing of a constraint dimensions were kind of bring talking about a B and this case D 1 of our starter with 7 that I would 9 dimensions based 7 so each constraint removed directions it's free to move in Frank Burke for that reason you can have in mind mentioned by playing this game over and over again with different directions associated with the compact space you can have deep 8 brain said rain peace explained always found cool maximum number of it you can earn you can just get rid of the freedom to move in any of the directions of space than what busy what would you call the brain b 0 0 these 0 it's a point or who at a point in space string is connected to and not free to move along any of direction that'd be 0 0 serves is 0 dimensions means a point from 2 0 bringing total B 8 brings it all makes sense and the role of their existence in some centers all necessary to the consistency of the busy don't brains are no kind of particle expected new kind of briefly a 1st for a safe for a F4 normal move no no no no no car you could have lost a wire moment Peshawar OK we played this game with a compact but now let's imagine having done this operation which imagine shrinking shrinking shrinking until it becomes arbitrarily small what happens on the side the it gets bigger and bigger and bigger OK so eventually on this side it can be so big that it's completely mistaken for a none compact for a nun compact venture other words a dimensional space is big enough for all practical purposes it becomes compact always demonstrated by this series of arguments is that even in the None compact corrections must be objects which are anchors of strength they can be oriented compact directions the Cami Oriental among compact corrections number and of any dimensionality starting with 0 enough to rule 8 dementia actually it got 9 dimensions but that means they completely fill space and that simply means that we're talking about open string theory in which the open strings adjust freedom move but Paramount intraday we wouldn't call membrane pleaser people called D minus 1 brings but you don't want to about their about your car OK so you start is 0 brain point in space and a string in can end where the other end of the string it could be on another 0 brain or it could be stretched out to infinity that's not a good thing because a becomes infinitely massive for achieving come back to the same point the St. D. Brown servicing a that these your brain what's the next 1 up a D1 brains and be wondering something very interesting about B 1 brain it's a wine now as you pointed out it does not have to be a straight line we deduce their existence in this way but once we know that they exist in once we know we're talking about a relativistic theory they have to be bendable their bendable can even then the around themselves on their structures were charred physically physical objects and they have strings connected but now let's forget the strings that connected them strings could be like let's forget the strings are connected to images just look at them this is a onedimensional object glued 1 brain a onedimensional object it can what's another name and among end didn't come back on itself what's another name for onedimensional objects like strain but are they maybe original strings know they're not original string Colby 1 brain and the distinct from the original strings How would you expect it might Gates trade attacks places not what remain may not have been deprived but that lets for that honor string of a much heavier in ahead then that makes a lot of sense because where how they start they started out as anchors like infinitely heavy things the holder strings down but not really infinitely heavy there there there there may ask depends on the coupling constants what depends on various things there have a much much heavier than the ordinary strings so in that sense anchors From but they are still line he said he got OAB report the range to restore firmer in our what's the next 1 up a detour brain be Tilayne is called the membrane membranes the 2 brains and there was forcibly sheets like tabletop year string in Conover around on a pair of strings Kimura like that is the a deed to bring Exxon up 3 brings a 3 dimensional world a decree brain fills all of this fills space center those basic space filling brain people and the villagers to space and if we have a D 3 brain than I would simply mean that we cannot open strings a could just move around there have to be a part of the brain the brain is everywhere and so it's just open strings a free will around everywhere so it's often said that ordinary open string theory string theory on a space filling brain but of a living in a world where higher dimensions that brain doesn't fill of space like 8 Tom brain and the threedimensional space the and strings Comeaux OK that's the idea Of Thee brains and as I said as I emphasized they are mathematically import restraint theory but they also are the origin of replication years a very quickly tell you what's known In a stolid 1 of these day book but a straight red contractor yes yes yet that's correct but but certainly correct Rod OK let's imagine
1:27:49
a brain commented drawn as deep to brain as Randy not ideal this is awfully slipped tho I really believe that this has to be calm not from the arguments that I and obviously giving you some road some sketches of arguments about whether string theory of the right period nature not the issue here the mathematics of this very our remaining many cross checks many many different things point mention our mathematical theorems of come out of it but mathematical speculations of been confirmed the mathematics of sorts it's remarkable and presumably correct 5 5 here's an a and be brain think of as empty and be means it has no strings and figures empty think of it as an empty space time empty space misplaced now is not a full space but it's just a surface in space but think of it as a space it's empty we put things into it we but strains until it like that often strings and these open strings are free to move around now tell you what to do with the basic process of them years the basic thing they can do is their endpoints result oriented strings so they have arrows associated with them when they it points come together in string theory endpoints come together Italy yes To win points 1 1 arrow coming into it and the other with an arrow coming out of it they can do the obvious mainly endpoints come together and lift off the surface and form a single string with 280 points like that I really think about that if these strings like this all of the particles which are free to move around and a string theory particles of strings is very much like the original open strings it we started with if we think of them as particles which are constrained to move on the surface of very close the surface then what we discovered it is that these particles but joint 2 of them could concur joined Inter won 1 of them could go out joining a separated the 2 were start to build up something that looks like particle process was starting to build up something that looks very much like finding diagrams showing coming in joint perform 1 baby hangs around there for a while and then the reverse process happens becomes too again were building up the kind the process sees the quantum field theory describes creation and annihilation of particles transmutation of the number of particles and so it mean it's not completely surprising that the mathematics of the interactions between these particles looks very much like quantum field theory In fact at low energies we don't have enough energy to really excite vibrations of the strings is simply quantum field theory where the particles of the quantum field theory of his open strings a the fact open strings behave like fulltime moving around on the surface the both times in the center of the pending mental theory that both times in the sense of a theory which lives in whose particles live only that the basic connection between brains In their applications studying quantum field theory on brains like this the following quantum field theories amid defined quantum field theories in exactly the way that I just described but now let some incidentally these surveys open strings connected to the brain he behaved do behave like photons moving around in the brain and behave like got 4 times and the lower dimensional fears but let's imagine now that we have more than 1 brain there is no reason why you can't have several brains for example parallel to each other yes the brain's parallel to each other you could move them closer and closer until they touch which case they just the former compound brain or you could leave them separated let's leave them separated from moment let's put 3 of them and just for fun 3 parallel brains rats and let's think of the kind of expectations that can move around well you can have excitations means ordinary string we're strange but given names as give the 3 threemile the 3 of these 3 of these names remains money give them or Red Star Marine what we don't know former were agreed to resist the names of the 3 brain Gaza guest for Waurika 7 at 15 but I'm particularly interested in having 3 of them what chemistry strings have we get a stranger to begin our red and not memory strings are also oriented give the mind the oriented and so what would you call this strain I would call it a read and I read or red red strain the Red red strain and they have for some kind of red raid particles we can also have Red Green particles Red Green particles awards would like that's where 1 man begins on red the beer and the other and hungry Hey so where we have were classify articles we have we of particles of labeled by tool indices cool colors the case of 3 brains we have 3 distinct colors that we have particles which are labeled by Paris of color 1 associated with outgoing and the other associated with income the sound like anything is seen before gone gone is a quantum chromodynamics as a bill for the 1st half as they say a brief maybe you should keep in mind this is embedded behind admitted a spate mimic that lets wine In the higher dimensional space that was no problem in order from here to here or from here I around here you're worried about passing through a half birthday a a well we have there are there will be some rules it will be some rooms and basic rule was the basic rule was really only 1 rule but we could use it over and over again on a Red Green strain what can I do it's a red red explores is going out here coming in here let's suppose this it
1:36:20
is going to have in a year I'm out here OK what can happen this sale to join with us and they come together and joined and form a similar strain widows always from here they yes another words the red and by a red thing coming into red in the thing going out of red 1 8 1 l conjoined and so simply make a single strength this is very much like a player like Eddie Green Beret glue 1 coming together with a red red 1 informing him of red green lawn seem rules exactly the same rules as our for blue ones but this strain cannot annihilate all lift itself off to served on the other hand if we had this situation here where to come together and they can lift themselves officer that's incidentally why Iraq 8 glue wants instead of money because 1 linear combination could disappear Rivera is stable Our so mathematical rules splitting enjoying are exactly the Yang Mills our quantum chromodynamics rules for OK what about for a summer what about work was a quarter of its language What is this language only has 1 color it's either they want impact it only has 1 color doesn't have 3 colors sorry doesn't have took a cholera impact of course must be a thing which only has 1 and look what it has language is a strain which it is on 1 of these brains and goes off to infinity now it doesn't really have to go off to infinity could go after some distant brain of a different kind but it doesn't have another and which ends on 1 of these 3 that's acquired as either a string coming in for a string going out when a string coming in and a string going out mean each other they can join in just disappear off the off the brain thickened jarring and disappeared from brain that's a violation of a court can mean court mistook works they can't Iowa they stuck and axis that's exactly the same role as caught the mathematical structure of the field theory that describe these things moving around essentially with some will act ingredients because of supersymmetry supersymmetric version of quantum chromodynamics and that is erm part of the reason that brains interesting for exploring quantum chromodynamics I'm not going to to show you how they used in detail shore knew what the connection between things power let's suppose is only 1 race but but it's not like quantum chromodynamics what if figure might be like now I have objects we don't after name them red red green blue it's just a just the a string His likewise like quantum electrodynamics has only photons it doesn't have this complicated who once structure these will be photons and well with these things John but they could be coming in or they could be going out in which case it would be electrons and positrons when come together make an irate 1 last point which is really quite fascinating remember I told you that there are ordinary strings and be these strings with no objects that we discovered is no objects which are a good deal heavier but they're also strengthen and interesting question is can these strain also in our brain right there sir incidentally I'm thinking about 3 brains because I'm thinking about freedom thinking about mimicking threedimensional space 3 brains really free rein interesting question can a D E strain but these days is itself something that ordinary strings can end but let's forget that can they a be strained in on a 3 Brainard 3 going into yes I'm going to try and prove that for you at a much more elaborate question but then it ordinary strained the ones we started with make electrically charged particles like the deed brains would be strings make their ends when they intersect video of the 3 bring here could you get me not well there are in some sense real but they are they gotta be something which is similar so what happens when ordinary strings magnetic monopoles truly remarkable magnetic monopoles a much heavier than the electrons because these strings a much heavier but magnetic monopoles are expected to be much heavier than electron become magnetic monopoles relation between magnetic monopoles electrical Mama polls in them in quantum electrodynamics is mimicked by the relation between these strings ending on these things and ordinary strings so I laughed toggle stuff expect that however photograph on detail but I'm trying to show you can string theorists which covered the whole war time to make gathering this didn't happen on 1 day this happened over a period of 20 years basically more no more and more than 25 almost 30 years of all these pieces were put together by various people of a wide variety of people who saw these connections and today string theory and description of and terms of brains is the primary tool for studying quantum chromodynamics it very bizarre the whole thing made a full circle or made a full circle from a theory our 80 runs to a theory of quantum gravity the presence of these brains were who was a necessary there which when you put them together In the end they mental space put together threedimensional be brains all of a sudden becomes the theory of quantum chromodynamics that we hear that the start so wraps I'm Norton described by described it as sort of mental gymnastics but I think more of them think it's a process of discovery in unraveling of the year of the mathematical structure of this bank is wide application acquire the former mayor and other quantum field theories are fluid dynamics all kinds of things so far has not had application would elect application forms the
1:44:54
particles spectrum and that probably because there's just a show it's do a photo him do it any
1:45:05
damage please our many Preminger please the who to but that eventually does warns of saying that use be brings him Iowa maniacs over her truce but it is the review of for food this poor is that this is a full list for 3 3 they see a lot the University of form are point of view with the 3 brains D 3 brains but if from some of the other kind dimensions which the people llamas world billion about premiums over here and had to be be strain no experience favism not seized is all set to ask for a meeting also warriors Rupert now there were also ordered to pay a gaffe came here were not a set without charge conjugation violation of feelings for us I had a few small car particle more interesting there are there are answers string theory a certainly has the potential possibility described the level of slowed in New York Columbia amenable they can have more complicated asymmetries allow that the store Compaq application of the law there's a lot of many many other object theory which are having gotten into misses these are the simplest of described there a lot of other construction other kinds of objects the period ahead of died and some some of them when they intersect are the ones break cemeteries the would talk with the can discuss them some of the time on an our energy and momentum the euro fly for more please visit us at
1:47:45
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Metadaten
Formale Metadaten
Titel  String Theory and MTheory  Lecture 10 
Serientitel  Lecture Collection  String Theory and MTheory 
Teil  10 
Anzahl der Teile  10 
Autor 
Susskind, Leonard

Lizenz 
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DOI  10.5446/15102 
Herausgeber  Stanford University 
Erscheinungsjahr  2011 
Sprache  Englisch 
Produktionsjahr  2010 
Inhaltliche Metadaten
Fachgebiet  Physik 
Abstract  (November 30, 2010) Professor Leonard Susskind continues his discussion on TDuality; explains the theory of DBranes; models QFT and QCD; and introduces the application of electromagnetism. String theory (with its close relative, Mtheory) is the basis for the most ambitious theories of the physical world. It has profoundly influenced our understanding of gravity, cosmology, and particle physics. In this course we will develop the basic theoretical and mathematical ideas, including the stringtheoretic origin of gravity, the theory of extra dimensions of space, the connection between strings and black holes, the "landscape" of string theory, and the holographic principle. 