Master class II with Juan Maldacena


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Master class II with Juan Maldacena
Introduction to the gauge/gravity duality
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Maldacena, Juan
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Publisher, Foundation for Fundamental Research on Matter (FOM)
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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.
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generally something and you had any questions or comments OK so the wanted to some eyes so we discuss this relationship between certain gage theories uncertain
gravity backgrounds I wasn't very specific in defining the gage theory so it's through best one-dimensional gage theory with maximum supersymmetry those who if you want I can explain to the more or if you're satisfied with this can't continue this I'm so it contains the young section with his gospel of some other fields and then we us this string theory in 5 dimensional and there a disgrace that I was the space race that's the new pricing geometry of the stupid that we discussed so of this kind of black ranks of revelry close to this mark rise from the described before the geometry very closely at this the geometry of 5 dimension and that's it that's where this came from and we had said that the politicians living by close to here with With this crime the are Mystery Inc 1 I should mention that uh what we discussed about the fantasy displacement so this boundary where the gradation potential goes to infinity corresponds to moment the western boundary corresponds to moving to the away from the and restoration so if you are tired object that has finite energy here in this new horizon Richmond you're very deep inside you will the very difficult for you to climb back out of this potential well and secure living down here and you don't have enough energy to climb out and so in the real situation where it in a situation where this connects to flat space this body is not intended the end of saturates at some point in the space continues and if you're doing deep inside in the bottom of this buyer looks infinitely bigger looks like you're antifreeze area space as opposed to the 1 with which was the baht yet the quality of life what is now known of Nevada yet so connected to the only notion black holes just so that we can salute here that what I'm talking about toilets are let's consider structure a black hole so that's the called everyone likes the knowledge of what it not everyone has this metric so this has some magic so far away becomes symmetrical flat spaces is this fear the radial direction of this fire become served 3 and here we have the wretched factor which is what we were talking about this threat this factor that becomes 0 the buckle horizon for tobacco affected become series this 1 that becomes 0 very close to the local rights only when only 1 direction 1 good considering for the nation's also charged Michael but under undercover metric which is very similar to this on With the minor differences that's a road disappear square this month their black holes which are charged and backers which outshot parametric which roughly speaking at the same point number but not exactly the same but the they have the same form in the sense that they have a single 0 at the height of the series of expand this metric around like went 0 for small that they're on type of this 0 so there this is the geometry of the New horizon relations and by virus by redefining the police come this looks essentially like flat space that those Lack of ordinary black holes and then you can see a charged black holes and when you have to have the calls to have the constrained at the northern promising will like this they mastered the equal the charge some units and when you take the extreme elements the geometry really develops a double 0 here so that this Indiana high price geometry has the form that Delta squared the Dow square plus the that square root of the square intent not really defined and and then there is this fear acquires a constant radius of the American and if we find that they could do 1 see this becomes minus the task square plus the BC square receive square and the magic office space which we can call quality to this is the two-dimensional and of what we were doing so the sense in which this black objects is different is that this extreme of Uncle it's closer extreme in-house this physically with it would mean is that the Hawking temperature would be 0 so this guy has non-zero Hawking temperature and this would have 0 hoping temperature of neither the sense in which it is different is that the black hole is localized in space the subjects are extended in states along the spatial directions right around for example 3 special dimension so in that sense it's different states black brand rather than a black hole but added that this the exactly the same as the sum hole and in fact this type of ATS basis appeared 1st in this this in the context of this extreme of black holes the have yeah question I'm going to and no 1 marcher something that should say to connect to what they discussed in the very beginning is that we discussed the strains that existing lashing gage areas where the strengths such as made up of some the correlations between the cost of the quirks this or the cost of an underground so we had the grew on-demand ignorant of this change they were the strings that worries some sense some kind of strings and they exist in any theory in any election theory the the limit and ghosts and for fixed land so Flanders fixed mandates to score and so when we call the coupling that make and cultivating make Geary small so that land fixed this regime there will always be strains and there will be weakly coupled the string interaction constants will be a further 1 Iran's Inc and their strength in the sense that the post aeration expansion can expand their free interference there the correlation functions and so on in terms of diagnostic and on the plane and the Taurus and so on 188 that those strings had the same as the fundamental strength of string theory that semis essentially those 10 dimensions strings but leaving on occur background so the strings the strings accuse are not the meaning for the mansions but they're living in 5 dimensions that that this was 1 of world that's an important point here they are living in has dimensions in the same way that all this In the same way that expectations here leaving higher dimensions they're made out of objects which are made up of compost their complicit here they're made out of many new ones and so on In there they really believe in this house high-dimensional space you can of course the description doesn't had an engine space it's not super useful if the radius of curvature compiled strength gains because we cannot solve it very easily and is more useful when there is a character sloshed which is that strongly coupled with so when you very strong coupling so square and much bigger than 1 then decide this is you can use cried the forget about string theory forget where he came from and so on so if you are only interested in Yemen's Theriot very strong coupling company about string theory can just take this and the calculations and never ever think about string theory unless you run into some problems and you need to remember whether those corrections are become an important or not and I was planning to add describing a little more detail how to I
understand the mapping states that you have on this side too the states of how here and there on this island was trying to make a little more precise this notion that for example a Groveton is a pair of blue on somewhat census a guy with a pair of blue trying to make a little more precise this and we can make this more precise by explained this in a slightly more than half of stock way which she's really the best way to understand that when you're dealing with the take strongly coupled systems so on this is so the followers of the 1st of what I meant explain theories explain right now is purely kinematics hits such as had to ascribe the the state's starts with a like amount of the need to find a convenience said of course and Senate comedian description for this so that the we can think of other than a mosque in the mostly away arms and 1st we need to think of all the states of young man's theory so what's a convenient way of thinking altered so as I said we create some excitation and excitation becomes very big so but it seems like we can keep track rematch of traditions about infinity the energy spectrum would be continues so it's not I would call the principal discovered from that point of view but the saloon last year when you have a system with master's degrees of freedom use would think those sometimes is to put the theory on and financial finite volume by the system on a box and then we get could spectrum and so on in this case the boxes 3 sphere so we can consider the government's theory or the theory and 3 sphere and and and in this case we we could consider that theory on and the ceiling there now we we could also viewed the Sicilian there so this circle here it's 6 3 and this line just fine and now it fired volley the spectrum of the the theory will be screened so for example if you have a free massless fields as you put it on this history well there will be a series of harmonics of the 3 sphere and those will be a series of this great ashes some managers now this victory is related to the picture of the play on the plane but and and it's it's useful to keep in mind this relationship because it's useful to use it to label the states that have brought by it on the cylinder so we give us a way to construct a stadium and in a way that it's very independent of the so the relationship is the following you can imagine a that you have our for nuclear force so here we would consider this to be UPN time around sometime this is considered to be cleared in time and then ask for a week we could do a devolution not that's occurring in ordinary Ukrainian time which would grind in this way but in nuclear and language runs along the radial directions and then and then essentially we ate them up to this picture because of rewrite the match against the US Squarepants square the omega-3 that symmetric for and we realize everything asked we writing everything they where so we or put out a factor 1st so this metric insight here is the magic of 3 sphere times line which is low far that style here well I didn't write books but this line would be Nowhere and so this metrics differ by underworld factors skin factor but if you have a theory that uh is skating Bryant and particularly also conformity invariant I didn't explain what conformity by answers that the people doing it explain it the I hear more announced than news so in conformance there is the trace of the distressed serious 0 so we changed the world fucked of the metric their demented we changed the nature by a number of factors their theory doesn't change so observables things computed the unchanged and so anything we computing our for it's the same must think of us during the same computation is 3 times higher OK now turn but equally they said nothing between all possible operators we can have a weakening said here the origin so operators the origin and the origins good mop to states here so different states that can run on a street that you can how honest 3 anchor for each so that the industry as a whole he respects of states for each state and the hero space there is an operator we cannot hear the origin and now this looked like a lot of states and also Limoges explained this in the context of a simple scalar fees that say you have a massless scalar field in our 4 so far in and you can he said you confessed 1st then do anything is said nothing here said something nothing here corresponds to here having the vacuum of the theory provided you can insert the operate the fire of 0 5 at the duration that would correspond to exciting here the field hearing the lowest the Colusa Klein harmonic harmonic which is constant atmosphere at this 1 little technical point and it explained so when you have a massive scalar field here here on this fear when you get this a scalar field that I use just the usual oppression in the sphere of glass 1 unit of class this land of must comes from the conformal got into the curvature and so on that a it's a technical thing that in order for this to work we need to have this month there is a very good reason for Allen that explain so this corresponds to taking this scalar field considering it doesn't in the sphere and discuss your anger momentum so it doesn't buy under this year it's like a harmonic oscillator in that time the action so that's a single Michael Lipper not agreements here their field so that was so this so nothing the thing corresponds to the icon's taking the field theory this corresponds to a simple 1 of these harmonic oscillator malls this corresponds to 2 harmonic oscillator moans 5 squared of 0 the unity of new 5 0 some other operators and corresponds to some other harmonic oscillator anew because now we're going to expand include 2nd harmonics in report .period expanding spherical harmonics on the S 3 and so for each stroke of money which harmonic oscillator and so on and the energy of the various states that has some ashes 0 this hasn't she won 2 it said that for response to this scaling the mention of his operator holds British behave under rescaling of course OK so that's that's history now with this this enables us to the looks like somewhat struck this dictionary and this is this is something you can do in any in any field theory has nothing to do with the gage character in any skating by inferior penalties the critical item although you can lose and the know on in any theory that the scan MRI and this is a convenient way to think about this now if we are now in the context of the gage going to other things that we can do 1 more color and we can clearly see this is something we can do anything University where we can lure unit theory that has evaluated well then the cylinder corresponds to his Simpson in the corresponds to the boundary of some way of writing ages 5 and wearing a symmetric Of the miners Koresh Ross
square it was clear that the euro Square last seen look at so so here we are assessing simply writing this and metric that we the road before but in a different set of coordinates
where it covers different regions and so on Newark as a different way of thinking out there yes 5 space here and viewed this as a the version of Fabius 5 spaced that describes best the theory on the Street and Tai Chi so in this way of thinking out there s based there G 0 0 bigger additional potential rises very fast to to the boundaries of here I'm just trying now was a solid cylinder so the boundaries of hollow cylinder only the surface of the city the 80 places the holes in the imperialist Limited and the additional potential a minimum at the origin broke with the CIA and the need arises you know actions to a particle that is here will all see later back-and-forth will not to infinity as he was going for there is a relationship between the 2 major spaces that they can explain if you're curious but for this point of view view this as too different ways of thinking about that here we see that the physics agrees with the physically expect on a
finite size books where on a fight yet on a sphere where the spectrum discrete server putting a particle a massive particle in the Balkans it's menu confirmation to put together both on we can take the same public excited and make it the oscillate back and forth and that would correspond to taking sums sort of excitation of this field theory and then oscillating this back-and-forth would correspond to having so that it is this fear on the boundary and when this is that a closer to this region of the sphere of the expectations concentrated more on this region that more concentrated on this region unless concentrated in that the operation and when it's oscillating in the other direction he concentrates more it concentrates much more in this region and in this region again and when it's sitting at the bottom of its concentrated everywhere and it's uniformly distributed over the whole fear good
I am in this way we can think about the various states and the various states are going to be created by operators so if we have an operator such as distressed denser team you know which is the trace of let's say they knew that I knew about them it said and the separator acting on the bottom of the 5th area will create the state if we have a weak company would create chest to new ones would create the Bruins mauling on this field of Lewis will be moving on the sphere with a minimal amount if we set that support the systems are the offender with whom we moving with minimal amount of financial on the sphere would create a minimal amount of vanishes state would spin to where the space of 2 rooms up to spin to that we could have that's what we have in the field theory in the gravity theory which has covered model the gravity so must this crowd and Masters wave that this oscillating between these 2 very additional potential wells and which carries the minimum amount of energy allowed by quantum mechanics and enabling you might think that the masses but the good perhaps action that's the minimum amount of action but this is a particle that is forced to leave in a space with a traditional potential well so it has to have some non-zero 0 momentum in the radial directions to have to have some monster ownership and its energy will be smaller and we can figure out exactly what the it's ashes should be be and for that we need a little more of kinematics so I I mentioned that the energy here would be the time translation symmetry me call this the square so we can measure and ashes would respect at this time on this pictures that this means we measure and ashes we measure and ashes units were the Raiders of the fierce 1 on the side that amounts essentially to measure an Ashes in units of lists of this time here OK and then if you have for example had a couple of more formula so you you find that they stressed that here are some scaling the measures as just as is that stress energy density in three-dimensional space units of and actually divided by volume killed good and actually divided by that energy-density actually maybe volume or length you so this is an ocean by lengthy Cuomo on this is 1 of link to the 4th against as units of 1 elected for 4 hours and stuff like that we call there is something we call an analyst at the dimension which and dimension is how many units of 1 of elected has and further stressed that for the nation's 6 4 and and what this means here is that we just under this follows simply from the fight stress energy density it's as being too operator that is concerned that there was a conservation equations that by some of whom mathematics that the know-how to plant explained that implies its dimension should be before I basically the same as this had this aggression would adhere to and so on the side they would have a granite on them would have a very long wavelength of 4 other than that the size of this potential awareness of the of the radius of curvature of Fabius space so that proper ownership describe it will be of the other 1 of our when we measure it with respect to this time which differs by an amount before the hour we find that the energy With respect to the stand out that we find here is exactly equal to to 4 and to do this properly requires solving their where equation for the gravity in the interior and which is essentially a straightforward but you have to deal with the indices and the message that you it can be done on but you know before you do it you know what resounded supposed to get because the rest of this year and by the same interest now understand where you can consider other operators and for each operator you find the correspondence that just for as an excellent simple expansion Amin said imagine you hope very particle of must and but the mass and here then the energy with respect to this kind of that article but would be essentially ended damn some factor father comes from the richer factory to improper time this kind of and that's a great but the 0 where these factors unique so we've got to have a hard time and so this will be the the corresponding dimensions of the operator in the boundary theory for a particle of Munson so From here you see the following so that if the masses if you have the dimensions of for the 1 like 4 6 or whatever and then it means that the masses compete will be goal will be going like some number divided by our right so this corresponds to particles whose wavelength is comparable to the site the radius of curvature I'm just trying to that the goal of what I'm trying to explain now is to explain the the because sizes were wavelengths of operators which have dimensions for the 1 like stress denser just mentioned for and they are objects which are very extended they have wave away function which is where is like a massless particles in its lowest state in a box of
sites are would have wavelength which is 1 of that's what we're finding appearance was consistent with the different points of view on just explaining this thing from different points of view it is being cleared isn't clear where now if you had a particle whose mask is much higher than the 1 where the Rios of curvature but then the corresponding would be very very would be very high so now so that's some kinematics and sympathetic where for example let that discuss this again after that question the string state inaction we want to address gravity so this strain is very small and the masses of strings are there is there's masses which here 5 or 10 dimensions and then there are the masses which are for the 1 on and they would correspond to mansions or an Ashes which are 0 for the out of the way by Ellis so you see that and to the extent where we can neglect the massive it's so neglecting the massive string modes will only be possible if the radius is much bigger than 1 string units that's was the condition for trusting gravity and that implies the dimensions of those states should be a much larger than 1 this is the gravity it's good nothing now you note that taps of states this is a gage theory I have to strike a balance playing on the connection between me and the weekly coupled her version of the game theory and from government well what we discussed the gravity of lending the indices confessed not plant the much and want to ignore the of so this is like trace after market that's that was distressed dances that had dimension for it's been too now there also some other operators which stand for which roughly speaking could be viewed as as they would've square ever could they have had weak coupling they have dimensions 6 and this is when she squares and much less than 1 and we can ask what will they do with strong coupling and In in ethereal gravity there no but you have to be a the being too but no no light particles of spin higher you factor in the interactions of Baltika ahead like public surprise been great very strongly constrained I mean both the that experimentally in theoretical so it's only fair that we could with approximation we don't expect any Masters part Marsalis has been part of if the dimension was exactly 6 its mass would be exactly 0 here on the right hand side and so if we 1 to do it with approximation 1 of the things that should happen is that the master of the particle has to be large of strong coupling and you can computed that so this 1 of you bitches square and something up for the she's grant so it goes in the right direction and now words would you expect the following further states as a function of London so how mentioned so that say we have 6 here many accessorizing linearly From this correction and strong company expected to rephrase fairly high know-how quite well it would be only that's a the 1st being for States in string theory comes from the massive string states which have muscle for the 1 that the strength and and they have this dimensions Iowa less and if you remember but you have to remember that when like some power sexually 1 4 of the of London but so this is the behavior very last longer than expected so this is what we should get if we can get from the string theory's weekly work From a strain moving on a space with radius of curvature is very large we get this from but the at their young males we get this type of abundance and you can ask whether we get in between now 1 of the recent Beckham 1 of the recent advances in the last the last few years was to be a to actually compute this core called Karabakh cycling so you can on the other the solution of of an integral equation you have to solve the question America label Yukon computers and matches beautifully the we coupling answer with the strong governance so this is concluded in the Danish limits on this limit lap angles conveniently with with the land fixed and you can't actually do the calculation so it's the uses the techniques of indelible models for those who notes with who knows what would that it's not and explained 1 thing that is useful for understanding when we think of this
as a traitor summarized the relationship between strains gravity and election limit in a way that it has general as possible so so in general would have the 1st 2 points the 1st is that when the radius of Fabius the various coverage of the spaces where you have engaged articulately it's much bigger than a then this is only and is much bigger than 1 now for them in readers of various serious anyway just curvature of the space that is what the Europe the and might end I mean the number of degrees of freedom on her 5th here at the end of the UN matrix this is a general property remember drama plant is what governs this the gravitational interaction say when what governs displaying expansion and so on so always seem not to have a gravity the was the 1st necessary condition is to have any much 1 always so if someone comes and tells you I have a guarantee the well of the ice Muller then you're going to a little skeptical because the gravity of the of the Ising model will be a very strongly quantum theory of gravity and because what governs the classical approximation to the fear of melodies how how different how different it elicits from a black and this is what governs the the extent to which traditionally waived a weakly couples said 1 2nd then we have the radius of areas much-feared analysts said I'm Indiana when there when the string length is whether is the final this will always be much bigger than a black market in this it will always be whenever there is some kind of strength and then on this implies that lumber is much bigger than 1 so whenever the radius of curvature speed the string size which is also necessary for in order have gravity approximation you need that the company should be very strong now you might have strong coupling and still not not necessarily have a space at this week a couple everywhere you do have it in any of before but but this is definitely a necessary condition so any theory that this has a gravity the world would be necessarily we will necessarily be strongly coupled and the reason it has to be respond GOP this because operators like this that has been how to gain a larger nations have to have a large dimensions and the way they have helped and how large Ashes is that the interactions of strong I mean the weekly coupled picture of this thing is just 2 Bruins mauling 1 sloshing back and forth and this sphere so that 2 Blossomwood independently and you increase the speed it means that the wounds mowing completely independently of each other as you contacted the problem and there is a strong interaction is stronger um caller that interaction between them that Bush's 2 and so the mental picture you should have used that theories that have you got me to do our strong active periods where many of the states or in the spectrum have been pushed the rate higher margins and you're left with a small subsector subset of the possible expectations of the theory they're smarter subsidize some will always include the Groveton because the stress Asher advances protected mansion and and maybe some other ones that the nuclease images of the 3 laws have something other questions all this and repeat this in no way going group this one's once more because I think it's important so there is indeed regime with large and gage theories will always have string was the string that might not be only some special circumstances are met like hike Copley this trend will would be approximated by gravity not to see these theory even larger intercity services with the last number of quotas would be a theory where land is probably going to for the 1 on land runs with the ownership the land that never gets done this area very smaller broader for the 1 the approximation of reality might or might not work because we're in the regime where Landis before for the 1 you just do the calculation and you see whether does work with us and work you don't have enough recent 4 for believing that it would work wrong and he works well for some cases and doesn't work for some other things there some things like the bulk viscosity that gravity abusive beautiful body for it in agreement with experiment and there are some other things like you know the the spectrum of vessels where you really need the strength mention the very beginning where gravity doesn't do a good job no I electoral and human remains to show you how to do something similar calculations also filed discussed generally prefer this and so on and crying out to feelings what they're usually called entries in the dictionary Soho given on a field theory problem how you translate to gravity problem I'm going to discuss a few examples just so that you get an idea given the idea for the 1st time I've ever discussed the very quickly Mariel just repeated in words that discussed how to calculate correlation functions of distressed concerns able stand by sending gravity restorations from the boundary and that and then directed the ball and you want me to discuss that demanded the likened that system for that well we couldn't find engage there is 1 sometimes it's interesting calculating expectation values of Western lobes this has some operators which are defined as the patenting of the Tichfield over circle physically with the ice chests I suspect motives of these things where there is essentially the face factor that this accumulated by a heavy probe work then moved along the controversy and in the presence of they gage
field this this quirk factor due to interaction with the good field we get an extra face facts of this form which will be influenced by all the laws that the running around and so on if you wish contains these all the facts of the radiation of this work and the interaction of the recreation of the quirk with their young fields with the caller electric field In QED revealed so you have just simply the radiation you can take into account by solving by calculating essentially this diagram the exchange of 1 photon and explain shaken and Dutch escapes to the conduction of the trajectory with a radiation but in theory wind directions is more complicated because you have some or all these kinds of diagrams and so the radiation itself interacts with itself and create some other variations on home and August this is related to the gravity of strangle 2 taking this conqueror now defined on the Monday so this is a pondering our 4 so this is for some contour and then you take a surface at the mention surface signal so that the ends on this contract the boundary of areas of the space you calculate you find that many malaria surface that ends on this contour and the expectation might have this with some look to nearly hour is given by the by to the miners tension of the strange times the area of the surface I'm and this has to be here which Jagger legal rights group London that history here string tension with strong coupling times the area In units where the radius of Fabius is equal to 1 because this is a purely geometric quantity that depends on in the geometry of the Contra nothing else and this is the whole dependence of the coupling of strong coupling of course there will be further corrections here before the war and less extensive 1 of group nominees this is history came for much 1 and the behavior for London much less than 1 is the same as the QED result you just take this leading direction and that would be when you neglect the effects of radiation itself no 1 thing you can calculate when 1 related calculations the calculation of the Corps command the potential where you take the court line and that the court climbed 2 . separated by some distance on the boundary there then in in the Baltic corresponds to a surface that goes between these 2 these 2 positions and the potential is computed as the energy of this strain or the actual length of this spring but with the ADS metric measure with the met manager with the flat statement and if we measure that the distance between these 2 with the flat space metric would get potential which would be leaning out but if we measure it with the ADS metric we did actually potential which goes like monorail so that the reasoning goes like 1 released because as you separate them or they go deeper and deeper into the interior where the war factor is smaller and smaller an you get the opposite the bonds and the 1 you naively would have expected and the dependence on land the first-run companies where the number hazard was here and for week up slander over so that's the same as the QED result multiplied the factory and because there and possible works for impossible Chuck quota charges for the quarter inadequate move the amendments In addition at a lower at a little more on this picture so many of you have a quirk so we discussed the DQ there for a quarter and that the court would get this call electric flex the destinies with constant vanishing and then this would lead to potential which is the tension of the QC the strain themselves in if this due status having constant that I shouldn't have In a getting by answering the picture looks more like with the 1 you having you know ordinary actual economics of the flag flies spreading everywhere and when you when start separating these churches that part of the energy that depends on the separation decreases like 1 0 on cost with minds now the difference between these 2 In the gave priority to auditing will be related to the geometry of the space than you considers the case that there is getting by and then you have media space you have this behavior always and that there will not be confining but you can have this case prematurely also for situations where there long the theories not Marion getting bias was useful for explaining the simplest In cases where you don't have Skilling Bayern's scale invariant then in these the behavior of the war factor because we had this wretched factor that was very large near the boundary pushing things too with interior but in the final theories what this will do is and will rise again or the space with dominate and what's important is that there will be many more value for this were factories is similar to what was happening with the war factor or the this factor sometimes called were factor sometimes called factor sometimes called very different potential there are closely related things for the purposes of this talk there on the same on you want you can ask the difference and so so that any object will be 1 to see that the particularity of for the case of a Pentagon with this means the following so recalled that the distance from here use the site right what this is saying is that in a confined area like this if you how an object will mean Maxus Energy by acquiring a specific sites and this but it doesn't want to Rexmont monthly be that's similar to what happens to the Broughton accused city where it it has given size the preferred size and curriculum by essentially the economics of of QC the kind of just the bullfighting dynamics of history in the mass of the problem doesn't come from the massive imports comes from the confining interactions of a strong the strong directions of QC but and the same happens for the strain matching you have this picture no we do the same thing but for restraint so that maybe there's an extra direction here and again so if we have
a string that is stretching along that special direction the whole string would want to slide down up until it reaches this minimum size here and if it's reaching some points on the Monday when OK when reached a point in the money here but in the middle we want to settle down to this minimum size so that medium-sized or that means that position in the radial directions corresponds to the sick room size of the strength and as long this it will give you a confining potential similar to accuse the history and finally I would like to and that is by discussing how and discusses some black over my namics of beaches the 1st is the 1st point I like to make this at this stage of narrative does not describe only and the ABS brakes describes the Sadia space with anything you can have inside on his quest disguise spaces that the asymptotic far away they look like and the space far away with the additional potential rises but in the middle you can be anything can have private can have blocked calls you can have whatever you want on the particulate and how black holes and an object that it's interesting to consider these 2 have the black rain then extreme an analog of the extreme about brain with discussed before then and I think it probably would not write down the metric so some metric which where we have the boundary so now if if we go again the additional attention too seriously so we have in rises near the boundary and then at some point at the but the glare .period goes actually to Syria and and he dubs a proper distance goes serially nearly so that has defined cooking temperature and so picture it thoroughly we can say that this would help the boundary and then we have the buckle horizon but at some distance see tasty Christ the horizon from the bond markets and today new features compared to the previous 1 is the 1st that we have a temperature so the previous based at 0 temperature and discuss the finer temperature it also has an a nontrivial for 1st of all this cooperation will not be boasting Bayern if we make this a preferred rest frame which is the best friend which and the subject is addressed and this earning the ball corresponds to the young man's theory finally temperature have the this theory where the Bruins are moving around giggling like you who wish should blossom our through it their strongly interacting so good in the past months with the misnomer but there strongly interacting and nuance and at finite temperature and they are supposed to be the same as this black hole at finite temperature and the entropy of this last month should supposed to be equal to the entropy of Pakistan and hoping of black holes which is the area of the horizon divided by genius this is their friend this is they go additional entropy of black holes and the just purely due to metric quantity that depends on in the area of the Black :colon well that they need to explain where this comes from yes well to explain my buckles have a temperature also appears that would take more than 5 minutes there have on Parliament has mentioned thing so if I tobacco's have a temperature which is related to essentially the slope of these are the the horror and Julio additional forces have here and the price the if you write down the 1st law of thermodynamics the the year equipped the free with the TV as well so the amount of change in the total energy for free and on the demand of total changing the internal energy a sequel to this change in the entropy but you know what the mass of the black qualities as a function of the temperature and then you can calculate the entropy and that gives to this former initial racing performance the formula for the reason the more complicated but the formula for the entropy and been nicer and more dramatic I haven't explained to you where the temperature comes from well the U.S. wanted to explain the temperature black holes and some analysts let me finish this story and another at the end you can ask so we have this entropy which is fairly dramatically classical comes from just a classic collection and this is supposed to be the same as the entropy of these gossip rumors that if you wear weak coupling you would calculate that safety killed and dimension an analysis and benefactor of offense square which measures the number of species you have people who have each grew and can have in this series that ran from 1 to doing this is the man from 120 haven't squared once they have this last time some simple practices by and so on OK so but when you compare the area you find that the area some geometric wanted and ends up being again the cube and divided by the sting Yukon and then you constant the coupling constant of the string gravity theory as I mentioned but when they won Renner 1 the coupling when Randy the composite score of the coupling of and squares so this is again also goes against square and the to have a very similar form but they have a different coefficients isn't weak coupling of the interest 1 it has some coefficient and strong company has a different coefficient forward to grow In her where to go for example better than the free energy as a function of London then we coupling has some value that's 1 and strong coupling has someone of 3 quarters it was really mean ever computed .period this aspects of the curves of the writers from coupling was the 1st correction values we postcards correction and in between is somehow supposed to Wilburton 1 of the other now associated in calculating something that strong coupling in this theory you can't calculated using the guy description right so if you believe in there if you believe in the relationship and you
just got greedy using the galley description if you want to check the description then you have to have the migration and calculate the sculptor that's not long would present methods had to look but and if you believe in their relationship than new shares calculated using gravity and you can calculate a bunch of things related to Earths thermal Of the show finding temperature density of books and nuance for example when he arrived for they discussed so far as they can Barbara this so we have the black hole completely straightened translation invariant but you could make a small obliteration on this on this back of for the week of this little wiggle would represent the a will of density so he had the flu is a little more advanced than some other positions and this week will expand then dissipate that's what you expect from what is the Blackwood fiction and of course the corresponding pictured finding temperature is the same story how the Yemen's theory with a bunch of stuff which has some density and that means this is the profile of the desert is constant but you can add little wheels and a few other we do this we will dissipate and will eventually go go back to equilibrium and it will have a non-zero so this this will were not postulate that it would do if there was no dissipation because this is a patient Association is dumped in this characteristic dumping time and and here and decide what happens is you have this wave near the horizon of the black hole and the wave forced into the black hole and the Wiley has fallen into a black hole in the system really goes back to a Gillibrand and to a uniform density so falling into the black hole is the same massacre liberation in the bond theory and you can make this incubation time for this long wavelengths estate additions and so on is dominated by the bog disgusted that which you can by share discussed consequences and this year is goes to the economy translated here into the absorption rate essentially of this Of these waves near the horizon and yet they actually very simple answer for this have softened for the for the subversion rate which is that social rate is essentially proportional to the area Of the black and the entropy salsa proportional to the area of you compute the difference with the ratio between the area and the the ratio between the viscosity on the entropy density and you find that this 1 4 Patricia simply a number and and this is a very low number which which which represents the fact that we have very strong interactions of the viscosity nephew it is very small when the interactions I'm very large because you need to His injections are a small you can always transfer a lot of momentum from some regional the fruit that is more than 1 Miller to a region that is very very far away very different velocity and this is a very efficient mechanism for transferring momentum across the velocity gradient and will give you a very large viscosity so very dilute gas would have a very large Misko then but very strong indirect influence has strongly directing us to be rerouted long has this very nobody discuss it is interesting it this non-zero I'm also interesting that when people do experiments at Greek and so on they see also very low by viscosity within this within this value to uh within our little money to that said on lost its value why it well any approach that looks stats from the weak couplings I would tend to be the election Shevardnadze because you stated the large valued weak coupling I don't think so maybe and maybe 11 rely on all the time so I was broadly here and open for questions or comments In fact perhaps because of that you like it or not not so great is his right under standard temperature of about called his European space officials of other colleagues varied from that point of view of the fact that there are lots of things from your standpoint of view that the Government will explain 1st president .period here and wedding-cake away from the principle interviewing them so if if you and the members of the black hole is related to a simpler a physical phenomenon which is the fact that if you are an accelerating observed something called it 1 would but Anderson's on the board so the point is that if you're an accelerating observers in flat space you will see a temperature to mention during the flooding flood space vacuum in a rocket and you then on your rocket and you start accelerating you put the thermometer through the window you'd see some temperature and on this temperature will be in proportion to the acceleration of sexual equal to acceleration units were CNH on and K the units normally set to 1 except the 1 OK so it's a very tiny temperature in 49 units I mean just to more physical ideas you translate temperature wavelength right 2 1 a wavelength and again acceleration also the 1 wavelengths than the temperature in the wavelength of the same lets the saying that they have to say more than that for the next iterations of this weddings are very very large because you have factor of C makes them very very large but anyway so the idea is that if you have an observer who accelerates very worried about accelerates and the constant rate this observer would see temperature now have can you list smallest qualitatively understand why you would see a temperature I want explained the explained it from the point of view of an observer with in Minkowski space answering because space and you have this guy here following this accelerated trajectory and he has at the moment there and disarmament there has let's say 2 2 levels right there were well in thermometer has many it's a system with many energy levels Manantial level so you have to that with so many energy levels and so has this physical system that
is more women across with him and is moving along and isolated trajectory and if you have a subsystem that couples to the fields outside and it's moving there are a lot like so exhilarating trajectory expected to immigration ,comma branched out on radiation and to have a chat at just article that small and you expected to immigration and have a couple of such positive charged particles that are more in your suspect that the inmate some radiation newly minted amid less than this the limits on radiation and that is roughly the mechanism for deletion of of this radiation is that you have some system here with several levels whose ashes can change you and assuming radiation and so due to the acceleration you let me bring them radiation that same branch of strong radiation is seen us by the person who is here as exciting or the exciting there the Ashley levels of this system has actually seen as temperatures can this requires some calculation that I'm not I'm not explaining perhaps
the simplest way to explain it is to on again resort to the UPN the European storage so here in order to make this exhilarating trajectory more manifest this communion to choose the continent of flat space in this way it is just flat space written in unfamiliar coordinates where trajectories of constant rule on this accelerated trajectories with various constant acceleration again if a fixed dollar move through this most of role which selected trajectory so here an observer was sitting at quiz accelerating uniformly as it were line which is growing but Rocio fix that some particular about this is suspicious centers of this according to Collins ahem never seen them where related to refute right and the plastics people sex sequence all he plants might stuff so this is the space in relation to eliminate the growth it was so that's this and now if so this is a time translation invariance situation to you can go to Ukrainian time and this becomes the rule square Lostroh square the sorry about put this minor send the wrong so this is the bank direction and so now we go to the and then we have the Indian In general the space would be conical depending on the radio .period a few clearly and so we we can and we will remove the conical singularities if wkt and identified with Doti and plans to buy and in and in this case we remove this conical singularities and then we get flat space so there which good ordinary flat Euclidean space now this is the correct thing to do if we are in Euclidean space because recalled that if we were to analytical accounting for all this Gordon and just go back to the annex courtliness and we continue to Ukrainian time then which is good the ordinary Ukrainians based company a new nuclear space the angle is it's identified would be beaded to buy but this on the identification of the angle from the point of view of this continent's looks like a finite temperature because its UPN time however you can pan with a finite period so so whatever you calculate here like a correlation function of fears at various times some positions will give and will give values which would be consistent with the UPN time period this at this time such that when you translate them with 4 and sometimes you get finite temperature results so he Fugue in Banda has circle when you translate Dr. Lawrence sometimes get fined temperature behavior cancel effects but in this perhaps more direct ways but that requires you the knowledge of you should know that if I ever despite the defeat cleared them as periodic than the time behavior will be fine temperature yes the conditions in which it is because of the yet to be English well I I expressed them in terms of land that which is square and yes yes yes yes yes yes that that the recent I explicitly the express line the readers that the combination that sets the ratio between the string tension on the radius of areas and that's a very physically important region David G. square young males is that the tender mention string company sold in Panama in distant the dimensional space which we remember right we have ages 5 and I never I never topped all this fear but we really have this fear and In this then the National Space they at animation string coupling and that's a good young males by the way I also never talked about that that angle so that Yemen's theories have that than that which is assembled 2nd parameter that's a 2nd muscles feel that we have in this this petition by physical losses to him than Americans so you know there's no known are not very efficient the opposite of efficient and yet it is considered is they mean what would you want to have obese considers the 2 layers are moving very fast with no transfers momentum that is flowing from across the velocity gradient you have a fluid that is flowing fast here and to fall from this direction throwing as fast we want to have no momentum transfer from here to there if you have weak coupling this particles it's a brother has a tiny momentum in this direction will travel for a huge sign up to here and then he will interact and the difference in momentum meeting hearing here is huge because of the difference in velocity and you would transfer a lot of momentum in that direction as 1st satellite so low some of the nearly literary century yeah but what happens at strong companies that so this gets bumped to something that if it gets the kids this guy and someone very close to here where the velocity is very also vary a similar to it's not so efficient that transferring the company they are transferring the momentum because the velocities where three-quarters I mean this this ratio here a sequence to 1 where essentially the mean free paths endurance of the desert comes all the way to fill In here


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