What Do CFTs Tell Us About Anti-de Sitter Spacetimes?

We consider the relevance of a collective field theory description for the AdS/CFT correspondence. Collective field theory performs a systematic reorganization of the degrees of freedom of a (non-gravitational) field theory, replacing the original loop expansion parameter $\hbar$ with $1/N$. Collective fields are over complete signalling a redundancy inherent in the theory. We propose that this over completeness is the mechanism by which one arrives at a holographic descripti...

These are introductory lectures on the correspondence between SU(N) gauge theories and Superstring Theory in anti-de Sitter geometries (AdS). The subject combines a number of different topics, including supersymmetric field theory, classical and quantum physics of black holes, string theory, string dualities, conformal field theories (CFT), and quantum field theory in anti-de Sitter spaces. We also discuss applications of this AdS/CFT correspondence to the large $N$ dynamics ...

We review in this lecture the relation between the Maldacena Conjecture, also known as AdS/CFT correspondence, and the so called Holographic principle that seems to be an essential ingredient for a quantum gravity theory. We also illustrate the idea of Holography by showing that the curvature of the anti-de Sitter space reduces the number of degrees of freedom making it possible to find a mapping between a quantum theory defined on the bulk and another defined on the correspo...

4D Lorentzian conformal field theory (CFT) is mapped into 5D anti-de Sitter spacetime (AdS), from the viewpoint of "geometrizing" conformal current algebra. A large-N expansion of the CFT is shown to lead to (infinitely many) weakly coupled AdS particles, in one-to-one correspondence with minimal-color-singlet CFT primary operators. If all but a finite number of "protected" primary operators have very large scaling dimensions, it is shown that there exists a low-AdS-curvature...

We note that the non-perturbative quantisation of supergravity as recently investigated using loop quantum gravity techniques provides an opportunity to probe an interesting sector of the AdS/CFT correspondence, which is usually not considered in conventional treatments. In particular, assuming a certain amount of convergence between the quantum supergravity sector of string theory and quantum supergravity constructed via loop quantum gravity techniques, we argue that the lar...

Much of modern string theory research concerns AdS/CFT duality, or more generally, gauge/gravity duality. The main subjects are a) Testing and understanding such dualities by exploring how they work for systems with a lot of supersymmetry b) Constructing and exploring approximate string theory duals of QCD c) Applying gauge/gravity duality to other areas of physics such as condensed matter and nuclear physics. I will briefly discuss the first topic.

In this paper, we propose a conformally covariant momentum space representation of CFT correlation functions. We call it the AdS S-matrix. This representation has the property that it reduces to the S-matrix in the flat space limit. The flat space limit in question is taken by keeping all the particle masses fixed as the operator conformal dimensions go to infinity along with the AdS radius $\mathtt{R}$. We give Feynman-like rules to compute the AdS S-matrix in $1/ \mathtt{R}...

We perform a canonical quantization of pure gravity on AdS3 using as a technical tool its equivalence at the classical level with a Chern-Simons theory with gauge group SL(2,R)xSL(2,R). We first quantize the theory canonically on an asymptotically AdS space --which is topologically the real line times a Riemann surface with one connected boundary. Using the "constrain first" approach we reduce canonical quantization to quantization of orbits of the Virasoro group and Kaehler ...

This brief conference proceeding attempts to explain the implications of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence for black hole entropy in a language accessible to relativists and other non-string theorists. The main conclusion is that the Bekenstein-Hawking entropy S_{BH} is the density of states associated with certain superselections sectors, defined by what may be called the algebra of boundary observables. Interestingly, while there is a valid ...

We provide necessary and sufficient conditions for a Conformal Field Theory to have a description in terms of a perturbative Effective Field Theory in AdS. The first two conditions are well-known: the existence of a perturbative `1/N' expansion and an approximate Fock space of states generated by a finite number of low-dimension operators. We add a third condition, that the Mellin amplitudes of the CFT correlators must be well-approximated by functions that are bounded by a p...