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AdS/CFT correspondence
About: AdS/CFT correspondence is a research topic. Over the lifetime, 6660 publications have been published within this topic receiving 355520 citations.
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TL;DR: In this article, it was shown that there exist smooth asymptotically anti-de Sitter initial data which evolve to a big crunch singularity in a low energy supergravity limit of string theory.
Abstract: We show there exist smooth asymptotically anti-de Sitter initial data which evolve to a big crunch singularity in a low energy supergravity limit of string theory. This opens up the possibility of using the dual conformal field theory to obtain a fully quantum description of the cosmological singularity. A preliminary study of this dual theory suggests that the big crunch is an endpoint of evolution even in the full string theory. We also show that any theory with scalar solitons must have negative energy solutions. The results presented here clarify our earlier work on cosmic censorship violation in N = 8 supergravity.
237 citations
TL;DR: In this article, a general and systematic treatment of multi-trace deformations in the AdS/CFT correspondence in the large N limit is presented, pointing out and clarifying subtleties relating to the formulation of the boundary value problem on a conformal boundary.
Abstract: We present a general and systematic treatment of multi-trace deformations in the AdS/CFT correspondence in the large N limit, pointing out and clarifying subtleties relating to the formulation of the boundary value problem on a conformal boundary. We then apply this method to study multi-trace deformations in the presence of a scalar VEV, which requires the coupling to gravity to be taken into account. We show that supergravity solutions subject to `mixed' boundary conditions are in one-to-one correspondence with critical points of the holographic effective action of the dual theory in the presence of a multi-trace deformation, and we find a number of new exact analytic solutions involving a minimally or conformally coupled scalar field satisfying `mixed' boundary conditions. These include the generalization to any dimension of the instanton solution recently found in hep-th/0611315. Finally, we provide a systematic method for computing the holographic effective action in the presence of a multi-trace deformation in a derivative expansion away from the conformal vacuum using Hamilton-Jacobi theory. Requiring that this effective action exists and is bounded from below reproduces recent results on the stability of the AdS vacuum in the presence of `mixed' boundary conditions.
237 citations
TL;DR: In this article, a catalogue of string theories which can be interpreted as Robertson-Walker cosmologies is presented, which correspond to conformal field theories on group manifolds, with the sizes of the Einstein universes related to the level of the Kac-Moody algebra and Milne universes also offering a geometrical interpretation of a Goddard-Kent-Olive coset construction.
236 citations
TL;DR: In this paper, an effective conformal theory describing the low-lying spectrum of the dilatation operator in a CFT was developed, which is useful when the spectrum contains a hierarchy in the dimension of operators, and a small parameter whose role is similar to that of 1/N in a large N gauge theory.
Abstract: We develop the idea of an effective conformal theory describing the low-lying spectrum of the dilatation operator in a CFT. Such an effective theory is useful when the spectrum contains a hierarchy in the dimension of operators, and a small parameter whose role is similar to that of 1/N in a large N gauge theory. These criteria insure that there is a regime where the dilatation operator is modified perturbatively. Global AdS is the natural framework for perturbations of the dilatation operator respecting conformal invariance, much as Minkowski space naturally describes Lorentz invariant perturbations of the Hamiltonian. Assuming that the lowest-dimension single-trace operator is a scalar, $ \mathcal{O} $
, we consider the anomalous dimensions, γ(n, l), of the double-trace operators of the form $ \mathcal{O}{\left( {{\partial^2}} \right)^n}{\left( \partial \right)^l}\mathcal{O} $
. Purely from the CFT we find that perturbative unitarity places a bound on these dimensions of |γ(n, l)| < 4. Non-renormalizable AdS interactions lead to violations of the bound at large values of n. We also consider the case that these interactions are generated by integrating out a heavy scalar field in AdS. We show that the presence of the heavy field “unitarizes” the growth in the anomalous dimensions, and leads to a resonance-like behavior in γ(n, l) when n is close to the dimension of the CFT operator dual to the heavy field. Finally, we demonstrate that bulk flat-space S-matrix elements can be extracted from the large n behavior of the anomalous dimensions. This leads to a direct connection between the spectrum ofanomalous dimensions in d-dimensional CFTs and flat-space S-matrix elements in d + 1 dimensions. We comment on the emergence of flat-space locality from the CFT perspective.
235 citations
TL;DR: In this article, the full dimension of the Konishi operator in planar N = 4 super Yang-Mills theory for a wide range of couplings, from weak to strong coupling regime, and predict the subleading terms in its strong coupling asymptotics were computed.
Abstract: We compute the full dimension of the Konishi operator in planar N=4 super Yang-Mills theory for a wide range of couplings, from weak to strong coupling regime, and predict the subleading terms in its strong coupling asymptotics. For this purpose we solve numerically the integral form of the AdS/CFT Y-system equations for the exact energies of excited states proposed by us and A. Kozak.
235 citations