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25

If we do an interference experiment with a (charged) particle coupled to the electromagnetic field or a massive particle coupled to the gravitational field, we can see interference if no information gets stored in the environment about which path the particle followed (or at least, if the states of the environment corresponding to the two paths through the ...


25

People hope that it may be an example of AdS/CFT correspondence that can be completely understood. AdS/CFT correspondence itself has been an incredibly important idea in the hep-th community over the past almost twenty years. Yet it remains a conjecture. In the typical situation, quantities computed on one side of the duality are hard to check on the ...


24

The answer is not known, but many believe it is: "Yes, every CFT has an AdS dual." However, whether the AdS dual is weakly-coupled and has low curvature -- in other words whether it's easy to do calculations with it -- is a different question entirely. We expect, based on well-understood examples (like $\mathcal N=4$ SYM dual to Type IIB strings on $\...


19

First, you need to reflect what, in fact, is a CFT. The abstract answer is that It's a set of correlation functions $\langle O_i(x) O_j(y) \cdots O_k(z) \rangle$ which satisfy certain axioms, like the conformal covariance or the short distance behavior when $x\to y$. These multi-point functions can be encoded in the generating function, so the same set ...


18

AdS is not a manifold with boundary in the standard sense (where neighborhoods of the boundary are diffeomorphic to neighborhoods of points on the boundary of some Euclidean half space). The boundary to which people often refer in this context is the so-called conformal boundary obtained through a conformal compactification of the spacetime. In the ...


16

SYK model provides us with the simplest example of holography which is much easier to study than canonical $AdS_5 \times S^5$ case due to much lower dimensionality. It was the initial motivation for Kitaev to study this model. Here is a set of 2 lectures in which he briefly discusses it. Because of its simplicity, it is easy to consider the thermal and ...


15

There is no doubt that the gravitational theory in the AdS space equivalent to the CFT on the boundary is string theory with all objects, effects, and interactions that string theory predicts, and this fact has been reflected in all the AdS/CFT literature since the very first Maldacena paper. This shouldn't be surprising because string theory is the only ...


13

I recommend you Chapter 5 (page 150+) of the AdS Bible, http://arxiv.org/abs/hep-th/9905111 Concerning your individual questions, which are mostly answered at the beginning of that Chapter, the additional Virasoro generators correspond to bulk coordinate reparametrizations that preserve the metric at infinity, but they do map the ground state to excited ...


13

A UV complete theory is one whose correlation functions or amplitudes may be calculated and yield unambiguously finite results for arbitrarily high energies. Yes, asymptotic freedom is enough for UV completeness because the UV limit of the theory is free and therefore well-defined. Whenever the coupling constant is small and the beta-function is negative at ...


11

I believe one has to distinguish two kinds of dualities. AdS/CFT, even in the context where it describes an RG flow (so not the pure AdS_5xS^5 case), is an exact duality to a four-dimensional theory, which interpolates between one well-defined conformal field theory in the UV and another conformal field theory in the IR. So holographic renormalization is in ...


10

You're right that the definition of a black hole based on an event horizon is non-local - you need to examine the entire future evolution to check if a light ray makes it to $\mathcal{I}^+ $. However, more local alternative definitions have been discussed, such as those involving apparent horizons: You basically define a closed two-surface to be trapped if, ...


9

As of 2015, there is a brand new book that's dedicated solely to gauge/gravity duality. The book is fittingly called Gauge/Gravity Duality, and it was written by Erdmenger & Ammon, based on a course that Erdmenger has been teaching over the past years at LMU Munich (although the book contains much more than be covered in a single course). Lecture notes ...


9

The BFSS matrix model is a quantum mechanical model – i.e. quantum field theory in 0+1 dimensions - that describes uncompactified M-theory in 11 dimensions assuming that we study the large $N$ limit of the model with the $U(N)$ symmetry. As myself and later Susskind determined, one may also directly interpret the finite $N$ BFSS matrix model as describing M-...


9

I think that the quickest route to the effective action actually isn't through string amplitudes, but through the beta functions. The conditions for worldsheet conformal invariance are equivalent to the spacetime equations of motion, and from these you can infer an on-shell effective action. This is all you can hope for in string theory (or any theory of ...


9

Similarly isn't the existence of space-times with closed timelike curves an evidence that gravity is also non-causal? Well, it's evidence that GR admits solutions where causality is problematical, but all the time machines I know about require stress-energy tensors that are unphysical. My own view is that GR is a superset of the real world, and as long as ...


9

There are several definitions of black holes and black hole horizons. You are correct that the event horizon is definitely a non-local phenomenon, and would not be measurable by a local observer. This fact doesn't affect the local dynamics of that observer, though, because she would still be inhabiting a locally freely falling frame, and her dynamics could ...


8

Not so simple. The equation $Z_{QG}=Z_{CFT}$ has to be interpreted correctly. AdS has a (conformal) boundary at space-like infinity and in order to define Quantum Gravity in AdS one has to supply boundary conditions on this conformal boundary. $Z_{QG}=Z_{CFT}$ is really a dictionary telling us which boundary conditions to choose at space-like infinity in ...


8

The example i know does not use 't Hooft's coupling, but i think it may address your question in a more straightforward way (i'll be "loose" with constants and numerical pre-factors, but will keep all the relevant info and details). Think of a 0-dimensional scalar field (bosonic $D0$-brane) with a quartic potential à la $V(\phi) = \mu\,\phi^2 + \lambda\,\...


8

Your question has many layers. The most comprehensive answer would have to explain everything about the gauge/gravity or AdS/CFT duality. Less ambitiously, there is a simple reason why a stack of D-branes behaves as a black p-brane. It carries a mass (well, the branes have a tension, the mass/energy density per unit volume), and if one has many D-branes, ...


8

The logic of AdS/CFT is independent of string theory, but one finds that the theories that have sensible AdS duals have a stringy character. You could hope to derive from conformal field theory that quantum gravity in AdS is stringy. A "bottom-up" way to think about AdS/CFT (see here, and references therein, for a recent treatment; also this slightly less ...


7

In principle, the AdS/CFT correspondence relates a conformal quantum field theory to a quantum theory of gravity (string theory). The key to the solution of all this confusion can be found in taking appropriate limits. It turns out that if you have strong coupling on the string theory side, you have a weakly coupled CFT and vice versa. The weakly coupled ...


7

What are the most precise definitions of "locality" and "causality"? Causality means that a physical process happening at space time event $x$ is the physical cause of another physical process happening at space-time event $y$ Relativist locality (in special relativity) says that physical quantities at space-time event $x$ cannot be the cause of other ...


6

The holographic priciple, as I understand it, is a general feature gravity has to obey due to its non-local behavior (as seen in the black hole entropy). These features should be there in any consistent theory of quantum gravity, and in this sense are more "general" than just string theory. It can in principle be formulated on any background, and the dual ...


6

I'm probably straying into dangerour territory here, but let me venture an answer. Doing so is probably just asking to be shot down by John Preskill, or some other such expert, but let me stick my neck out. Despite Ron's comments, gravity and EM are different in this context, in the sense that you can't flip the sign of the gravitational interaction the way ...


6

It's not a "$G(2)$ lattice" one has to compactify the M-theoretical dimensions upon (after all, the $G_2$ lattice is 2-dimensional); it's the $G_2$ holonomy manifolds. There are lots of different topologies of these seven-dimensional manifolds. They're analogous to the Calabi-Yau manifolds but don't allow one to use the machinery of complex numbers.


6

Since 1998 or earlier, there have been no doubts that the AdS/CFT correspondence provides us with a full non-perturbative definition of string theory on the AdS-like background, including all of (type IIB) stringy objects and interactions and subtleties that we have ever heard of. An obvious reason why the CFT can't be equivalent "just to supergravity" is ...


6

The factorization of Large N quantum field theories is explained in the following review by Yuri Makeenko. In vector models, factorization is easily proved using the saddle point approximation of the path integrals. The matrix case is more complicated and requires examination of the symmetry factors in the Feynman diagrams. Large N theories can be ...


6

D-branes are not restricted to planar geometries. They can take on many different forms, and you often encounter branes wrapped around spherical manifolds, like $S^1$ or $S^4$. To determine whether a given configuration is stable, you have to evaluate the action of the D-brane configuration, which is given by the Dirac-Born-Infeld action. For a $Dp$-brane, ...


6

The fact that the boundary theory is conformal means that renormalization does not induce running of the coupling. However, there are divergences which have to be regularized and renormalized. The regularization requires the introduction of an arbitrary scale, which is not Weyl invariant and leads to a conformal anomaly (in even dimensions). Correspondingly,...


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