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.

AdS/CFT duality for non-relativistic field theory

Abstract: We formulate a correspondence between non-relativistic conformal field theories (NRCFTs) in d?1 spatial dimensions and gravitational theories in AdSd+2 backgrounds with one compactified lightlike direction. The breaking of the maximal SO(2,d+1) symmetry of AdSd+2 to the non-relativistic conformal group arises from boundary conditions on bulk fields, without the need to introduce non-vacuum sources of energy-momentum. As a check of the proposal, we use the gravitational theory to reproduce the NRCFT state-operator correspondence between scaling dimensions of primary operators and energy eigenstates of the non-relativistic system placed in an external harmonic potential.

Supersymmetric Index from Black Hole Entropy

Abstract: For BPS black holes with at least four unbroken supercharges, we describe how the macroscopic entropy can be used to compute an appropriate index, which can be then compared with the same index computed in the microscopic description. We obtain exact results incorporating all higher order quantum corrections in the limit when only one of the charges, representing momentum along an internal direction, approaches infinity keeping all other charges fixed at arbitrary finite values. In this limit, we find that the microscopic index is controlled by certain anomaly coefficients whereas the macroscopic index is controlled by the coefficients of certain Chern-Simons terms in the effective action. The equality between the macroscopic and the microscopic index then follows as a consequence of anomaly inflow. In contrast, the absolute degeneracy does not have any such simple expression in terms of the anomaly coefficients or coefficients of Chern-Simons terms. We apply our analysis to several examples of spinning black holes in five dimensions and non-spinning black holes in four dimensions to compute the index exactly in the limit when only one of the charges becomes large, and find perfect agreement with the result of exact microscopic counting. Our analysis resolves a puzzle involving M5-branes wrapped on a 5-cycle in K3 × T 3.

Causality in AdS/CFT and Lovelock theory

Abstract: We explore the constraints imposed on higher curvature corrections of the Lovelock type due to causality restrictions in the boundary of asymptotically AdS space-time. In the framework of AdS/CFT, this is related to positivity of the energy constraints that arise in conformal collider physics. We present explicit analytic results that fully address these issues for cubic Lovelock gravity in arbitrary dimensions and give the formal analytic results that comprehend general Lovelock theory. The computations can be performed in two ways, both by considering a thermal setup in a black hole background and by studying the scattering of gravitons with a shock wave in AdS. We show that both computations coincide in Lovelock theory. The different helicities, as expected, provide the boundaries defining the region of allowed couplings. We generalize these results to arbitrary higher dimensions and discuss their consequences on the shear viscosity to energy density ratio of CFT plasmas, the possible existence of Boulware-Deser instabilities in Lovelock theory and the extent to which the AdS/CFT correspondence might be valid for arbitrary dimensions.

Large N matrix models for 3d N = 2 theories: twisted index, free energy and black holes

Abstract: We provide general formulae for the topologically twisted index of a general three-dimensional $$ \mathcal{N} $$ ≥ 2 gauge theory with an M-theory or massive type IIA dual in the large N limit. The index is defined as the supersymmetric path integral of the theory on S 2 × S 1 in the presence of background magnetic fluxes for the R- and global symmetries and it is conjectured to reproduce the entropy of magnetically charged static BPS AdS4 black holes. For a class of theories with an M-theory dual, we show that the logarithm of the index scales indeed as N 3/2 (and N 5/3 in the massive type IIA case). We find an intriguing relation with the (apparently unrelated) large N limit of the partition function on S 3. We also provide a universal formula for extracting the index from the large N partition function on S 3 and its derivatives and point out its analogy with the attractor mechanism for AdS black holes.