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Master class I with Juan Maldacena

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Master class I with Juan Maldacena
Introduction to the gauge/gravity duality
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We introduce the duality between quantum gravity in spacetimes with boundaries and quantum field theories on the boundary. We describe the arguments leading to the relationship and the dictionary between computations on the two sides. No string theory background is required.
Keywords gauge gravity
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welcome and so I was this attempt to start here resistant to stand against Army and then try to give you a general idea of what the gage gravity qualities so basically the Gates credited while at this relationship is antiquated between 2 things 1 is a quantum field theory there are a theory of quantum interacting particles and when such a quantum field theory is equal to a gravity theory he said relationship between 2 quantum theory so this would be a quantum gravity fearing and and the way we currently have of constructing quantum right fiercest a string theory so this would be strengthened and the relationship will have the character that they gravity theory in the interior of some geometries have some geometry which has an interior and some bond be more precise and explaining what this is and so the gravity theory inside will be the same a quantum field theory that lives on in the on the bond in this mission so you start with a quantum viscerally military on the surface of a sphere and you get the idea .period Amin also in the interior of sphere and so that would be a basic relationship and really try to understand that the describing the more the whole book will be about understand in this relationship this is a conjecture relationship that is supposed to hold on various there's a lot of areas for the relationship and it can be used in any direction can be used to understand gravity theories if you're interested in understanding about theories some black holes and so on you can use it because you can't might understand quantum field theory in my freedom of some quantum field theory and then you'll understand gravity or alternatively there are problems in front of the theory which is difficult policy quantum field theory but they become easier and the gravity of the character of the nation relationship is that things that are difficult he can sometimes become BC on the site but that's the motivation now I tried to explain it so I to take some steps back and I'm going to describe something which is there with happens with a series of major cities in the large and limit then limit that then and thereafter the Matrix becomes large so machine the contraction and now going to try to explain 1 point which is the connection between large and gage theories and the strings so I'm going to connect Josh and gage I'm going to say that these 2 things are connected strains of strength on this is an argument that this fairly all the goes back to the 7th despite dolls and goes as follows to imagine a theory that contains matrices so we have some major which have some industries by and injury and they transformed under the group you and say this matrix can be multiplied on the left by a UN transformation from the right by by the inverse of the year and transformation and it could be various things so it could be a sign in the other remain tresses and then we'll have some action which depends on this matter said in a way that invariant and the the group you it could be just their lovers single matrix so would be just a single matrix in the simplest example assistants in the matrix and they're listening to over the end square components of the nature of the Matrix single matrix and then an action which could be that the traces of M Square is a very simple of gulls sending thereof so we can put here compliment that just for fun with interest be scaled the this and nothing changes so this is a sequence of just there also were simple and the we could make this a little more complicated by I think something which would be good quality directions for example and in Cuba ,comma and and in this circumstance than this GE would be the coupling and you could expanding patrician various you would go for a single single at the edge of cigars and and then you expand these you bring this down from exponent and interest expense In the coupling you're probably familiar with such expansion and so the examples there are are other examples which in group include for example matrix quantum mechanics which could be just the matrix of harmonica at hopped oscillator just to make it so now it's a abutting the one-dimensional but until until the time of could have this year and some squared and these the series the standard that the blast the commentator with a 0 at 0 would be a gage field and so here they transformations the gage transformations are so here the global transformations that their the change conduit in the matrix and by UN matrix here where have a local gage transformation it's a function of time and the other on the role of the gage field chest impose a single conditions to take out of all this harmonic so this is a sequence of this a serious this is a collection of and square harmonic oscillator and you can each harmonic oscillator transforms from the U.S. and you can conceal the states that are annihilated by the UN symmetry so UN singlets and you can see a suggestion that stick the physical content of there so it's also simple and more complicated example is young males theory which could be a theory and did I mention that saved what could be space than the mentions for example of the forms traces of army and where know is the usual expression for the field strength in the yen males major the euro thank you ,comma data and you so hear in new a new Rochester and by in major since new adding this is the primary the fourth-best and variables space demand is considered the threat
on :colon world so this is the action for the theory and the new the fucking there last year usual and Angie's the coupling cost but in no 1 interesting thing is that this serious and in some ways to simplify the diversion limits in the limit that the number of the rank of a matrix of racist sometimes and called the number of scholars and the name comes from the fact that this this theory in the case that NEC was 2 3 and we take the gate repressive 3 times this year .period of Miami which describes hero here the eye of the particles described nuclear arms anyway and that property was "quotation mark caller historically and so that's good crumbling hammocks for any the 3 sometimes this is also collection Cromwell anemic this is being parents well I guess this is very clear for you guys let's hope it's good for everyone have now and so I want to try to explain why this series simplifying the Russian women and the some as they become classical the become classical become and maybe some means 1 property that the classical theory passes that and if you take the expectation value for prowled the functions of the models this expectation values of the classical state there would factorize liturgy of B & Q there would just be careful .period Q the European can so expectation value each functions in the so if you have a function with a well-defined B and Q so this will be true In this case but what happens is that if you have the operators which are a single traced so trace of a bunch of mattresses so here aides multiple Teixeira there could be a product of various other
matrices words for example it could be that the F Q you take an rates of some of our then and such correlation functions will come with factories into the correlation function just 1 of the traces times the correlation function for the other traits some operators and the basic reason this happens is that when you I consider such an operator you will I consider this expectation by the ZCU when and perturbation theory you start track in the fees within each trays and each of the fields would carry a collar and the and you can think of them as a kind of "quotation mark with the collar and then :colon know that occur with a cross in the corner with developed and then that if you contractual then you'd have to contract with the collar of 102 color of the other an if they are contracted within the single trains so when you end up doing on the contractions you will get a factor from from some in or the straight similarly here however when you contact the field from here to there you will need to call correlate the index of the Straits would mean that the praise and so you will use a factor of friends so that index ended was riding here and was running around values that gave you factor and you would not have been the case that you "quotation mark you gotta correlate this In a case that you consider it appears that doesn't thought completely factor the only contract within a single trades you would have this factor friend extra supporter offense and that its reduced indicates the new contract to separate presence and so it that's a purely kinematics thing it doesn't have anything to within directions it's it's just how you contracting this is adjust their entanglement that is present in this and this is here how Europe summoned over this and this so there is an extra be interesting thing that happens when you consider the interactions and this may be discussed the looming on the dead so on you the president perturbation theory with young or something that has security direction me we could even be this theory here and then leading are there you have just the free propagation of the particles were equivalent users have the outstanding their earlier how the standard Fiske the integral and this represents the correlation function for the Palestinian people and is this matrix feel an idea could be a major basic order and decorum and going to the known by so I it's the color and and going this 1 transforming the fundamental essentially the fundamental Europe of you and I went in and the and now you consider interactions and so when you consider interaction you can draw diagrams that where so this this double line that diagrams will be like fine and NYTimes except that they are also keeping track of how the indices are contracted with was referring here 2 women talking about the construction of the innocence of for example you was there was something really Cianjur world will end here when the news Cianjur but this index here in the middle could be an index gained the bronze from 120 and so the whole result of this item would have this thing is for the 1 this will be a for the she's were on the G 4 each interaction at each of and and for the number of course at this writing here and it's time we increased the number of callers if we keep doing that the diagrams on the plane Will here we added 2 pots of tea and we had another powerful and so will get them out of the park oranges grants so that the spectacle diagram will go lectures granted when they won a group before we go and in this way and you see that book have this form however that non-playing GM or not a lot of these so and for example if you mentioned you well it seems that we could draw a very simple 1 could be to consider a correction for example to appropriate the test formed in this case we had this factor and remember that we had the effect of an environment around the loop here we don't have it because we have the side and so well here in this case which has kept there and quality and this is the simple answer me OK so majority we could take this doing this is that come out here and we could essentially joined them buckled here and if you you were to do this properly you would find that and in this case there will be only 1 boundary so we stopped here and we go on around the hologram we I never encountered Free Index so this was that and will be down where we be of the same or the this amendment but before the G Square Square sits down by power of 1 or so the call that dialectic expansion can be separated into playing and diagrams which are the diagrams who can run the plane as the once I drew before this 1 is headed to growth comes out the black we're gonna be drawn playing another planet diagrams and have a form of G square and while the non-playing and diagrams I'm down by parts of whenever and square so this is the leading 1 they can be drawn on in Toros and as you go to higher genus surfaces thing of all things with candles and so on you have lower parts of France now the fact that I did diagrams can be separated into playing and I'm playing and is a bit of reminiscent of string theory was in fact exactly what you have a string theory where you can consider that they leading contributions to some process that involving strings come from diagrams you can run the planes and then dials you cannot draw on the plane at corrections and I think it's a very basic view of string theory doesn't tell us exactly what string theory suggests that says something that looks to the mention there this there is something to look into the mansion now this looks like an abstract painting that the thing that looks to the mention precisely this chain of particles so you have these particles which where you have a color and Dakota and they're all correlated to each other and the form and this kind of chains now hear this line said as nothing other than this sum over the indices the each of these particles can be traveling in space separately but the indices are correlated so you have you might have created let's say 2 Bruins here that start moving away from each other but if the indices are correlated therefore ministering in the sense anger so the object doesn't need to be small for less need to two-week-old has is not holding together this 1 plus one-dimensional this two-dimensional nature one-dimensional space like structure but in the eyes and there's talk of 2 were one-dimensional so it's wonderment 1 space dimension one-time dimension because that both the strength and other shape and he said there was space dimension is set correlation that exist between the cost of this by the courts to have any new that it could be mowing apart from each other and there's a correlation between the color of the and the color of someone the next 1 and so on and when I say the 1st and the next day that need to be there could this this that have to be the closest to this 1 they could be far apart from each other so you could have and have no 1 here and grown here and I'm on here and know here and I 1 here and there mind that follows is winning ,comma space could be this way
and then this 1 and then that 1 that 1 and 1 and 1 for example what the families with this line size how the quotas are correlated and what happens is that when the could these 2 callers correlated the interactions between them on the hour lecture by a factor of 10 then interactions with colors that are not correlated so in Yemen's theory essentially to the northern the only particles that attract the ones that carry the same color exactly the same core index and if they are they're far from if the colors here here we have a sum 1 of the colors here would have another sound the same general not this to Gaza Moss for most of the bonds in the sum they're not going to be the same so interaction between these this particle in this particle for example the reduction will be in this part and that part of it it's clear that people but also the whole point of this is that in the latter limit the very general proper thing is that they the particles have a kind of two-dimensional structure is not nothing space in this space of callers this for a long this has nothing to do with the structure the having in physical space Of course if the Pentagon said tract as judges and and the charges attract the mean electric bus reminded the Select doesn't mind of electric chairs that will attract and so because of the dynamics they might choose to form something where spatially a quota of 1 would be attracted to land the color of the other and then they might form dynamically something like the strength and could I know that that but that's a question of the dynamics got exactly what type of object that the form will be a question of the economics and but this is the basic question about even the kinematics of of the future of the interactions in the plane element hockey so that don't have the cancer strings this that appear in Russian gage they seemed a little mysterious because live in this scholar space they to have something to do with there motivation for introducing them was to analyze the government's theory where in experiments strings of St. you have excitement here Spanish whether higher matches compared to the ashes of the 7th on new excites strings and this 6 strings were seen in experiments and that's was 1 of the motivations but now what what this world I should explain perhaps a little more work another flawed and meaning of the word strength so he areas this were straining every use meaning adjustment in this corner correlations between father of that's going to start the word strings in the sense of the usual collection of string theory and tried to give you an idea of what the string theories about commercial string theory we talk about this strain and now will mean something stated that looks slightly different from would be met before and so forth for our current purposes this train will be a one-dimensional objects physical objects which carries attention and and pricing Moscow unit length that's how you practice and strength for example a violin strain would have some tensions and some must be lengthened this characterizes the long wavelength constellations of strength so here and have a string which is in philly things so everything is going well and from this point of view and the tension is equal to the mass screening length and this is what's normally cholera the 6 trains who had an excitation industry with problems and and stretch that you make is more litigation withdrawal the speed of light on the Wallstreet so it's almost the same as a violin strength except that the extension is much bigger than the tension of the usual violin strains and that's why the excitation drove faster than the travel along the violent storm that's the strength at now if you had on such a string you could consider its motion so you could take it closer to a string of this kind then you can you can let it evolve so I can write down the equations for such a strain which are similar to what you would write provided string the photo from an action which is equal to the area of the the pension times the area of the lower volume spun by its strings of most space-time you should find there the solutions by minimizing the complexion which is very similar to the action you right for particle and well then you have proceed as you would proceed for well you could find a quantum version of this so you could quantized this strange I mean that simply are 1 way to do it would be to seperate the motion the classical emotional straining to normal modes so different from other monsters who for a system with many harmonic oscillator Sisulu for that's a violin strings which have many installation lots in the New quantized each installation more individually the as mother physics where you have all the possible oscillations of a solid menu no 1 dies the respondents the forms is the quantum of observation is the same thing on so you have all the normal modes and you can't and then would you expect to have so you have this sole loss elated things that would have upon dice oscillation and actress so if you compute the anything we've actually compared the new you find that that the spectrum of possible entries were masses actually simple in terms of the mosque where the money goes like some indicia divided at times the strength tension the string tension sometimes is defined in terms of 1 over the string length they just a definition of what strings like this events string tension on the strength as dimension for constant which is the tension of the strings in units of 1 relying squaring units where each part and series with 1 1 and so here again on the same quantity appearance and you think of the string length as simply said set in how big this this subject these 20 self-selecting so-and-so Slayton and not excited too much it's it has sums characteristic size which is a form of string length OK now and besides looks so pretty modest number very said this should not be surprised at conditions some oscillating thing is quantized simple physical systems no 1 curious thing is that there are when you go through all this there are some things that would formerly have mass equipped to 0 some states that minimum oscillations states have must the 0 and some of them have speedy but to to so you think that such a strain oscillating that would correspond to an object that looks like a massless particles Moussa's like and it has been acquitted of others exactly the quantum numbers of the gardener gravitational waves which have masses there must listen has been acquitted now when interest in property of gravity to independently of string theory or anything like that is the following selection you are and you have a massless spin to particles and knew postulates some interaction for that he postulated the most general interaction you could imagine a leading Northern narratives with means that the leading nor the lower national direction of these particles and in such a way that you can think of in such a way that directional list contains the direction you expect from gravity and that is to say that if you have a gravity wave then there this code going to gravity couples to the gravity with couples to the inaction of the Woods's have to gravity waves that tracked each other a little bit because as you expect from gravity
so he just postulate that this of the interaction between so you have a gravity wave right and he interacts with a gravity that meets a long-range gravity field which adjust to the new world here I am Monday Wayne something I suggest postulate this interaction then the whole structure of the theory just fix all the nonlinear trends in the action affects the you just get uniquely the structure of general relativity so that's of this section that's a very interesting and important property of gravity that just knowing the lower lower national just knowing this a three-point direction you determine the rest of the nonlinear interactions Of course it's a connected so this is 1 way of there being gravity and of course is connected to the fact the structure of gravity is fixed by Genetic Alliance and so on so it's it's very constrained Platzeck aside comments so he in view of this comment you wouldn't be surprised if I told you that if introduce some interactions between the and then you consider the interactions of the Stringfellow ashes as long as these interactions are somehow consistent the sugar-producing the structure of General David and in fact they do so if you there's a simple way to introduced the interaction between the strings which is saying that the strength of fixed priority of splitting into 2 so in 2 pieces of string across the canvas splits and can reconnect that space-time diagramming looks like this I'm behind this this picture there are precise mathematical formulas that we'll need to get into but that there precise formulas behind this and you can with this farmers who can compute the interactions between strings and then take the low ash limit by lower Asher limit I mean and Ashes let's that whenever Our list then this string tension that the the the parameter where discussing that's the same thing it's the same thing and then and it's 1 Ashes mean direction of the same as those of General this was my bible of string theory trying to explain string theory 1 the backward other questions figures announced Open for Questions please don't buy yeah this is less than the string tension so depending on what the string tension in the western means different things so if we have a string tension which is TV would be an Ashes last-minute TV string tension was implanted would be less than implied it's a string tension is an EVA would be less than a week so it depends on the physical publication would have for this for this objects and this time the answer people would have given you and then the years ago would be the distinct action has to be of the order of the guts tickets that that was the leading model for how to connect string theory to the real world but we won't have to do that and we will see that we don't have to amended that the string tension of the QC the strangers is lower than that this 1 GB so where during the strings of accusing the word wouldn't set in the string tension 3 GB never the kisses string 1st of all ,comma as we see we should not think of them as living in flat space so that changes will be this discussion which this formula for example was suspect strength in Plattsburgh where and 2nd the all in for the QC strained there the interactions between strings are strong our reasonably strong so you had included directions to the right physics so states can break for example Corsica gives to the strain viewed you can also understand kisses trainees work what joins a court can antic work 1 so if you have a core and they their core electric flux lines that go between them in her father lines and as opposed to electromagnetism where these lines spread everywhere in space In his you for narrow tubes such that when you have separate them by B & the amounts they give you a constant energy density per unit length and so this duo is something Hamilton which behaves like a relativistic strength similar and it's similar to the ones I was talking about In fact this this this spectrum of most of the spectrum describes well the spectrum of sons of high-speed so make a lot
of you know sometimes people plotting them right from the word go with friends Square of Geroge should take the speed of the masses they all lie and nicely along the straight line as this discoveries indicating they go up from here on it's been 1 of sp 1 up to speed 5 OK so lonely very good now the simplest string theory too but 1 more thing I need to explain and connected to your question now we say that string theory describes gravity a lower Nash's at the nation's less than the pensions but now string theory has a new parameter here which is the coupling this drink up the strength of the direction so when we have here therefore it simply waiting for the mentions we would have given you constant which has units of blank squares and this year than cost and will be proportional to J. squared times the strangling square so for break even if you fix this string length for very small gene new coffin with a very small so in such a theory would have to landscapes 1 is that the the landscape at which quantum gravity becomes important which is applied and they're 1 of which is longer landscape which is when gravity gets corrected into strength let me see if I try to if this is lit landscape and the reason for this is 0 % flunked dining and there could be a less which is bigger and if you're trying to if you're going with a microscope when you're looking at the sun particles you would see that at this distance you'll start seeing strength and before you get to the basket and abandon wedgies this could come much earlier than this amount will see no applications what's the relationship between the 2 now connecting to what I was discussing here 1 I discussed there was this expansion in Jena so expansion in how complicated the surface of interactions 1st ranks itself here is custody .period interaction but we could consider for example the scattering the tale of 2 gravity waves would be described His string theory by diagram like this and that there some form of attendance and this is the contribution that has that the polish of his fear and then the corrections that I will discuss little and this corresponds in the particle description in the protocol limit this corresponds to a bunch of fine and items like this would be the leading 1 I grow but this 1 with the correction correspond to look diagrams he gravitates to quantum corrections to and write the corrections this to this process and intergrated this would be this this type of violence and the Russian by the string theory their finance and that's 1 of the nice aspects of string theory that that gives a theory of gravity that this but there at the refinery that is finite and brought Richardson Her now so what you should get from here is that there is some theory of quantum gravity and which is described as this spring the Office of which will you need to know all the details but planting your at picture that if you want to keep in mind is the following that if we have some space which is scary and we have the Gravitt you anything theory would be .period like string theory is the little things that has size ls gravity would be with approximation as long as the radius of curvature our is much bigger than analysts so long as this happens Yukon and many fear uninterested physics which happens at for the you can forget about string theory and you can use I think the so and on introducing strength adjust to help you understand when you can forget about it and when you can use clearly I think there is so you might say well why way into the Senator from when have to forget that well hopefully will this will become more clear that the latter questions yeah 1 of yellow I'll get into that I mean when we get to the finish I think this is the time to get from but the thing is to find out I will not that that was the thing that was nightmare on
died in presented correctly this spring diagram this is 1 without the look this is was this imam diagrams and then and then I drew the problem is they drew and then there is I think I said a confusing way and this 1 with a looping pass was the fine and I remember the look and no question so strings give you gravity again when this happens consider this happens you can go from strength to gravity and forget dollar strength so if you don't want to knowledge strangers for the murder of however there that the recently introduced strings was to try to explain why there is a connection between between gravity and quantum field theory that relationship with the very beginning explained that get the expendable I mentioned that I win a date engage serious there are some objects that look like strength strings 1st because they're the strings in Codorus placed 2nd innings series like you see the action physical strength of the mention experiments on the strings not obviously related to the strength and talking about here not too obviously related I mean the strength and talking out here at the beginning there was at least that is lost leading mentions then fled the mansion for his demand that Europe faces that if you this strains have delayed flat space then that I mentioned should be equal to that of essentially that some other Russian with 26 that let me concentrate on that and the mention 1 and to make the theory really nice and simple the theory should be having signature which is called supersymmetry F for now for the purposes of the stock supersymmetry would simply be uh some nice thing that symmetry that makes the theory especially so yes they could thus this practical simplifications are 9 might be the severe of nature in there there are some reasons for thinking that supersymmetric theories on nicer but for the
most that's a practical point of view can just say that interest in this was because they're simple to solve now so this then the natural and string theory besides goes containing strings and contains some other objects which of course will call the brains this is some kind of membranes that this theory has the kind of cosmic defects of ,comma Kaufman right In such brazen and such cosmic defects and sauna arise in other theories like interferes with the potential of the could be the main was before that the separate regions of different different bodies of the scalar field but here you have this objects and the nice thing they have is that they are described by simply saying that the expectations are given by open strings that analysts what this says is that in the same way that for applause strings we had massless being 2 particles for open strings we have Marsalis has been 1 particles and if we have many of these brains so that they would have end of these brains we have the strength that can start from any brain and and than any other brain and so would have associates that have to investors and interactions among the subjects it's been 1 objects again are constrained by the same interests and I essentially the launching directions are essentially uniquely given by Yemen's theory for the same reasons in gravity and so when you have these subjects to take the lower again no 1 actually means an Ashes less than the spring you have yeah ministering to a theory with this Lagrangian so you have these subjects which had lower lashes are governed by a young man's there but this certainly objects which have some tension and so they can have the space around them and there is an alternative view of this the brains which as a source of gravity and they would cover the whole space around them and they will give us some space which ways than the National Flood space and nearer the object is some Paris-based some or should that looks a bit like a black hole so it's extended along the dimensions the brain's extended so if we have a brain whose where volume means three-plus one-dimensional and so it has 3 extended special dimensions then you on this where volume you will have for the National young Minnesota 3 spatial and one-time young mysterious and and so that's the from 1 point of view so you have bring forget all about the open strings so this is some object that has the young man's their living and now forget all this before that where they came from and we just have be solved so we have 2 points of view on 2 2 views on the same thing we have a lower Nash's we have Gravitt also very low 1 ashes with interact very weakly so doesn't very weakly underwent office the lower the ashes the less they interact with each other so winning decorated with this brain and so we just basically have this option young as now Yemen's theory him for the nation's police classical in its scaly Marion and so they interact with the strength which is independent of the now on this in this picture would have relatives who live far away and then we can have relatives that fall into the near horizon region of this black hole Netanyahu restoration you and you have an important effect which you have any black coal which is the phenomenon of Gretchen so if you write the metric for this subject to the state and metric is the it contains some functions so I along with the press 1 dimension you we have 2 different factors when multiplies the 6 or thrown the mentions of the brain and To along there were William dimensions and this is some function which you can calculate that and according to the attention of the brains instantly about you can calculate and he has this form OK now gold medal the fact the same for them but 1st the 1st brush so that the important point here is the following that when ice very small the safe is a very large and this factor is very small that is something always happens when you go near Blackwood independent of the function is that the factor multiply expand action will become very small and that's the signature of a horizon is that the time factor is becoming the factor multiplying the metric is becoming very small
that means that and what that means is that that the energy secede from so there's proper time so the the U.S. is the proper time and then there's some factor it's colleges 0 0 square the juice 0 0 that multiplies that related to the at times measured far away this means that all that and ashes measure far away that is because and their related again by the same factor to 0 0 and the ashes measure would respect the proper time the proper he said the energies an observer who sits at the fixed value far measures because of for example he could have a little let's say this this is an observer of some US and because salute particle that measures some must and according to him and let's say he hasn't broken sitting near the horizon for black hole that same problem has seen very far away will have an energy which is very very tiny because these factors were want this happens whenever you have buckled horizon this begrudge and his contacts with it means is that is there any question about it this is what is 1 of the most important lesson the whole discussion it's important that this understood well so right so we are in this room and we're falling into a black hole and we measure the mass of these things some number of kg the site of several made like but some others and that makes us but the sitting very far away from the buckle Reisman would see the same object has been much like the OK so there is this factor that becomes very small and what that means is that if you're very close call this excitation that are very close to the buckle horizon look from the point of view of an observer was far away they look as if they had very low when ashes so then here we have 2 things that have lower Nash's 1 it's all the 6 editions near the back of harassment and the other 1 is all this fee is described by young men and there if you just assume that these 2 things are the same as describing the something you get the and engage gravity was so which says the Louisiana's theory now you forget where this came from entering variant of the whole brain discussion and so on and you just the way things that do launches Japan's 1 on 1 side we have a young males description of engaged through descriptions of this is in the best one-dimensional and contains UN vegetarian this is a four-dimensional quantum field theory and in for the mentions should be equal to certain gravity theory In our string theory if you like feeling like they were strained unite for the moment the theory being that 10 dimensions and the 10 dimensions are given by the particular geometry 1 the Senate's 5 and 5 comes from this fire sphere thanks 7 space which is "quotation mark 5 dimension and untested space and went to explain what the business sector so gravity in this space is the same as Yemen's there on the spot could yet 1 of the early years of the yesterday it is that you don't have both still have these and in addition that that was the idea so people in the beginning they thought you had both there that the well it said should be true because this is the most reasonable thing that could be true once you get at and you have to know should this and the thing is that from this point of view shows have the young description and it's a complete description of the system so you have a guy can come scene becomes CMS leaders of free rent and here you seem to have more to have more complicated things but then and you realize that but it could be that this cooperation is maybe it's describe at the center of this by the same this cooperation is described the center's success this young man's rich and indeed if you yeah yes all I know it doesn't yet so when well let's that's why this relationship is useful because and their Hamas's vision of the blackouts so yet so it's but the idea is that the presence of the black rice on is related to the fact that young males and is standing by and has the use of and very very low when action that you have a theory so whenever you have 1 of these notion
theories where International Ltd there is isn't gnashing got it is very likely would have block horizon In the do-or-die description well I would say to the more precisely and and if you computed Torricelli's 1 people but we started doing good calculations of literary absorption of gravity Celtic from this brains and and another ,comma finish of these brains and various problems of all these rights and and comparing the 2 sides and we noticed that they gave the same answer and then on I haven't centers give the same answer and that it is and that they are all the result of the week if they get the same answers when we were taking their ownership limits and when they did give the exactly same answers it was new to to another property which is the fact that that has to do with the regime of validity of various approximations of this theories are supposed to be exactly equal but the radius of the space and so 1 year for the radius of the sphere of space in spring units and for some reason is the 4th power the 4th powers numbering bring forth a sequence the young his company here attempts and so this relates the quantities that appear in the left and the right hand side to some quantities that appeared in the left hand side it's possible also "quotation mark no if that you can easily do calculations here you can easily do calculations here when Jeanne to square and it's much more than 1 because then hold this looks was strong in the very beginning can be neglected and you have the preparation of the free particles if not you I to do is attend calculate them final the formalism is
complicated and so this is my when burst aeration theory it's about it's a marker inapplicable and you can calculate the ceiling on this side is when this happens here In principle you have strengthened this background but well as you it is new year no exactly how it plans to strengthen this backgrounds on the EU now and many years ago not now more is known as explain what none but this is for pretty difficult if the radius of
curvature cemetery now is the radius of curvature is very large so when our reliance is much bigger than 1 right that was the direction we would forget about string theory just think of gravity and you just look at this as a a solution but the growth solution of some system of the the National equations and you can analyze those in and see what those coming simply and so that's the regime where this is assistance so this is Sissy Wenger's young males is much bigger than 1 so this is when I answer for the so when this is much bigger than 1 this is sustained when this is much more than 1 this site is it's so this is 1 of the the things that makes this relationship difficult the testimony because when 1 side insisted :colon vice-versa but it's also something that makes makes it useful because when 1 he can't calculations on 1 side become music aggressions on the other and so on and so was mentioning some decorations were not even the same as in the recent in the sentences because 1 was then when GM was very small 1 was stunned when GM was very large and some of them they didn't have to give the same answer even tho their relationship is strong arms said was the original motivation and I II to limit I haven't it's explain what they basis is yet another explains in 2nd before I like to mention 1 of thing and so there is this parameter the land something's got biblical land there which is to square and and when when it is very small opposed to we have young man's preparation theory I'm just going to re-emphasize the same thing that I was discussed when he sees the 1 we have some no-man's land where no method is correct and here we have the regime where gravity 60 I'm going to hear this is clear this that there with them meaning by this now this whole thing Everything Is this training areas or string areas strings on this background they can describe all this vision of a few knew how to solve strings this spot and by now people know how to solve only some aspects of strings on this backgrounds and you can calculate something's mostly as they go from 1 side to the other and check that the 2 sides matches they're supposed to much no can broadly discussed some attractive slated for have sometimes yeah yeah I know you yet to be was by you meanwhile yes yes they yes yes I mean yes yes the question was right right there good so this this and this and important questions well then perhaps the best dancer and most of must correct this to say that the spin when Boston is really not not completely observable because it's not gage invariance it's not costing the tests chestnut color and just a single often is not observable I and so that's what that's why you don't directly see the gage bosons that that that is correct but Selanne said this fine because you still you used to have we like to have some of the cases can occur being 1 let like the Boston I so that's 1 point 2nd point is you asked me about this being too and they mention what distinctive saying it's 1st of all in the course this being too is not right of survival in the center of the city announced in the sense that the in Crumpton gravity the uh no no local lobster rolls so is this is something that that's not surprising the 1st time you hear it but after a while you get used to higher local illustrations space you cannot find a well-defined of sorrows and the well-defined Monday resource of service only measure far away where their fluctuations of geometry number large so in this context the only observers that we have here are defined and the bond of this I probably should have explained a little bit better with EDS is before answer your question but that limit try anyway and so he spaces some space that has 4 the mentions the 4th set for the measures we have here and then some extra action and that some some boundaries and the boundaries of the far away in space this is a region where quantum gravity fluctuations of suppressed and you can sick and a solid platform from which you can do want to merit experiments so you can sending gravity waves and UPS or gravity waves from this position has been to bother the best you can it gets from the speed
distinct about the concern is the possibility of calculating probably the litter competence and extending what happens when you send somebody considerations and brother and so you sending gravity waves and you ask what's the probably did display than they become too gravity waves for example or to send to gravity waves and they become 2 other gravity waves these are in the gage theory they correspond to correlation functions of the stressed that so you you take 4 points in this case 1 too 3 and 4 and you make took 4 insertions of distressed Spencer and you calculate ladies in the field theory so stressed that suggest the ordinary stressed answer for young men there and so the new new the sequence of the trace of the new about that I knew about that -minus the trace them and so that's the usual stressed answer for Yemen's there and if you compute this in the atmosphere in use in fine diagrams and so on is supposed to be the same as it was when you get from this week to brother I where you can say that they stressed that Israel has been to particle is basically like to spin 1 part so the state created out of these 2 spin-one particles which is not the Coliseum to spin products for the morning far away from each other and corresponds to a gravity wave that is falling In 280 estates materials I think I've tried to explain that nothing is 2nd only to be better but I question has different degrees of what President I'm attributes the spike in a again another vast isolated and if you're not satisfied and I'll try to give more I tried to explain more work yeah but it is very important that we cannot objective about where we we should not match things which are not getting married so when Channel philosophy of philosophical point is that gage symmetries are not and not from fundamental wanted this of the theory has but their just simply redundant the redundancies of foreign description resonances of description and so we shouldn't be surprised we don't find the Gates the gage degrees of freedom now I know about something which is a little more physical which the gage bosons themselves and fossils they answer them individually but you could see them in a single ladies of correlated for example that 2 correlation function something that have singularity correspond to the exchange of very moving 980 space that would group in this case that actually corresponds to a situation where when you make some points approach you have a little piece of string so there is some object here Woods some strings and a be so strained that approaches the boundary moved fast between 2 points on the boundary so strained that has that is more aggressive on the morning fast that's something but fairly close to engage post was CEO Fugate was not the reason I say fairly classes because In offered to begin gage Boston you need to be a weak coupling weak means had occurred and so this is this would be correct if we are doing in dealing with the strengthening highly cars based on the metallic Hallock airspace the string splits into various business each of which more independence and a cities in the exact the more exact solutions that you get by the evidence well I don't I give more OK so as any other questions canal either gravel more space which was bombed the only Valparaiso ADS spaces the following spring to have flat dimensions and then you have an extra dimension I and you have a share Richard factor which multiplies sold all of these dimensions equally which is 1 overseas squares was just stressed that the Phoenician but has Sara proper this this space is uniquely defined by this but this problems solved some interest expense now 1st of all the and the space environment and the when of course is American the .period Monterrey symmetries so he'll any Punk'd transformation here rotation both translations this imbalance in the same way as Selena for the mention spaces but the nation has a signatory under the the rescaling of both X and see so if you risk in both of his government this metric is invariant loses this double symmetry that means that this space looks the same and providers of C so if you see that the 4 might have seen look that the space is the same you will
vanish the space would not notice at which 1 of you the same way that you cannot say at which 1 of the absolute position your because the spaces translation by however the space has a bigger additional potential which is the Gezira 0 I got Drescher factor but they could also have called it rendition of attention to something and that the sharp increase in net sequences 0 so what this means is exactly what you think it would mean that if you have a particle that and tries to move here with you think will happen and you have the additional potential buyers imagine you have you have this space has begun additional potential barrier and there's a particle coming in from the left investors buckets so we will bounce back and any nasty but the coalition's bounced back in so and that's what we have I had this vision at sea but the 0 this version of a small cities is called the boundary of space no not this notice the funny thing that so I I mentioned the fact that all all all observers see the same difference superstitions but nothing this season big forced the worst letter writers of the market is similar to being in the gravitational field of the Earth where it doesn't matter how high you are list in the the approximation you was the and IT field pushing you down and you have this kind of translations symmetry in the sea directions but I knew what is symmetric is defined you always have the same force and you can tell how high you operations measuring the presidential acceleration listed in on is the same thing except that here is exactly every week every observer here is said bigger additional force pushing it through the city the letter amounts of C I'm amendment and I said big but and it depends on what the radius of curvature of space is so very the radius of curvature is very very small this is where it will be a very gentle force Bush and so on ,comma contained now clown so that's that's this that's the space no 1 question you can ask is on with started with the four-dimensional gage theory which is defined in three-plus one-dimensional and we ended up with the space which is passenger you 1 plus an extra dimension so what is this secular mentioning the gage theory and the basic idea is that the extra dimension of the value of seeing these precise of an object on the boundary on the boundary would have we can have that's it we make an excitation and that excitation perhaps some characteristics size and as time progresses this excitation would however be ambiguous size that's what you would expect that happens this theory of this case so this excitation withstand defusing and becoming bigger and bigger ,comma and for all that even if we don't ask what with the dust amicably if you have some it's edition of some size and you up like a skin transformation which is a signatory of the theory you get an excitation which is related by symmetry of Asmara sites so this to its editions which are rated by symmetry the rescaling symmetry of the therein yeah I should probably have explained the fact that yet atmosphere in the best mentions With supersymmetry we now supersymmetry with maximum supersymmetry at this scheme by and so it's drastically action was getting but with supersymmetry is also looks good humor and want mechanic and so the Celtics additions in the theory that are related by the symmetric and in the bark they correspond to the 2 and 2 expectations which are at different positions of the sea variables so that this figure 1 for example response to some values he 1 and the smaller ones that say the red 1 which is mother corresponds to some other values and the bond there too particles of exactly the same proper precise the proper size and the bulk is exactly the same they're exactly the same particles and they other cold and they only differ by their position in the CIA actions such as the kinematics underlying Onyx is also the same so the fact that he had raised this additional force pushing them to larger bodies of C is the same as the tendency of of must spent the ghost to want to become more and more extended just the problem further you can't just there with this stuff most altered the speed of light and this political sources that the more women and that's how we translate this too the things now now we can't even explained the origin of this extra dimension so the following land only if it's so in the 1st chapter of the London elicits Mechanics book they talk about the action for protocol and a few rather you know we really Wednesday is the mechanics and on and that he says the Ivan it from some Johnson intra principles of says well you have translations symmetry ponderous symmetry with the action from massive must this protocol being where his as well monster election can only be this With 2 derivatives and so on now we have something which is the subject which has both possesion size let's call this icy and From the moment that ignore them the fact that it's simply that we will get in the end but some size and we're glad to ride the monster election we can have a consistent with the signatures of the theory the symmetries now also include rescaling symmetry and if you think about in the same with the same energy of land the leadership's Lipschitz you will find that this is the most general election you can write down company some parameter here and this is indeed the actions you get 4 for a massive particles in 8 years show just there it is simplistic and you can write and this discussion more Morris who is more mathematical the sophisticated statement which is that you want to classify state cynical form of inferior and use it using the representations conformal group and the same group classifies the states of particles the union ADS space and misrepresentations saying one-to-one correspondence but they really burst onto the same qualitative argument this this arguments we haven't pointing out here amid strictly speaking this ominous on the when the semis very large highways you have to use the wave equation but their argument is accepted as well so this explains why the list gives you an idea for a white wall Hawaii you expect this extra dimension yeah wired list is not so strange to have an extra dimension the questions this I I think we're supposed to stop at some point maybe this might be a good time construction than what time would like to start the 9th not so that's but something like