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.

Relativistic CFT hydrodynamics from the membrane paradigm

Abstract: We use the membrane paradigm to analyze the horizon dynamics of a uniformly boosted black brane in a (d + 2)-dimensional asymptotically Anti-de-Sitter space-time and a Rindler acceleration horizon in (d + 2)-dimensional Minkowski space-time. We show that in these cases the horizon dynamics is governed by the relativistic CFT hydrodynamics equations. The fluid velocity and temperature correspond to the normal to the horizon and to the surface gravity, respectively. The second law of thermodynamics for the fluid is mapped into the area increase theorem of General Relativity. The analysis is applicable, in general, to perturbations around a stationary horizon, when the scale of variations of the macroscopic fields is much larger than the inverse of the temperature. We show that the non-relativistic limit of our analysis yields the incompressible Navier-Stokes equations.

AdS black holes, holography and localization

Abstract: I review some recent progresses in counting the number of microstates of AdS supersymmetric black holes in dimension equal or greater than four using holography. The counting is obtained by applying localization and matrix model techniques to the dual field theory. I cover in details the case of dyonic AdS $$_4$$ black holes, corresponding to a twisted compactification of the dual field theory, and I discuss the state of the art for rotating AdS $$_5$$ black holes.

AdS3 Holography for 1/4 and 1/8 BPS geometries

Abstract: Recently a new class of 1/8-BPS regular geometries in type IIB string theory was constructed in arXiv:1503.01463. In this paper we provide a precise description of the semiclassical states dual, in the AdS/CFT sense, to these geometries. In explicit examples we show that the holographic 1-point functions and the Ryu-Takayanagi’s Entanglement Entropy for a single small interval match the corresponding CFT calculations performed by using the proposed dual states. We also discuss several new examples of such precision holography analysis in the 1/4-BPS sector and provide an explicit proof that the small interval derivation of the Entanglement Entropy used in arXiv:1405.6185 is fully covariant.

Lectures on Conformal Field Theory

Abstract: These lectures notes are based on courses given at National Taiwan University, National Chiao-Tung University, and National Tsing Hua University in the spring term of 2015. Although the course was offered primarily for graduate students, these lecture notes have been prepared for a more general audience. They are intended as an introduction to conformal field theories in various dimensions, with applications related to topics of particular interest: topics include the conformal bootstrap program, boundary conformal field theory, and applications related to the AdS/CFT correspondence. We assume the reader to be familiar with quantum mechanics at the graduate level and to have some basic knowledge of quantum field theory. Familiarity with string theory is not a prerequisite for this lectures, although it can only help.

Bulk locality and boundary creating operators

Abstract: We formulate a minimum requirement for CFT operators to be localized in the dual AdS. In any spacetime dimensions, we show that a general solution to the requirement is a linear superposition of operators creating spherical boundaries in CFT, with the dilatation by the imaginary unit from their centers. This generalizes the recent proposal by Miyaji et al. for bulk local operators in the three dimensional AdS. We show that Ishibashi states for the global conformal symmetry in any dimensions and with the imaginary di-latation obey free field equations in AdS and that incorporating bulk interactions require their superpositions. We also comment on the recent proposals by Kabat et al., and by H. Verlinde.