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.

Deep learning and the AdS/CFT correspondence

Abstract: We present a deep neural network representation of the $\mathrm{AdS}/\mathrm{CFT}$ correspondence, and demonstrate the emergence of the bulk metric function via the learning process for given data sets of response in boundary quantum field theories. The emergent radial direction of the bulk is identified with the depth of the layers, and the network itself is interpreted as a bulk geometry. Our network provides a data-driven holographic modeling of strongly coupled systems. With a scalar ${\ensuremath{\phi}}^{4}$ theory with unknown mass and coupling, in unknown curved spacetime with a black hole horizon, we demonstrate that our deep learning (DL) framework can determine the systems that fit given response data. First, we show that, from boundary data generated by the anti--de Sitter (AdS) Schwarzschild spacetime, our network can reproduce the metric. Second, we demonstrate that our network with experimental data as an input can determine the bulk metric, the mass and the quadratic coupling of the holographic model. As an example we use the experimental data of the magnetic response of the strongly correlated material ${\mathrm{Sm}}_{0.6}{\mathrm{Sr}}_{0.4}{\mathrm{MnO}}_{3}$. This $\mathrm{AdS}/\mathrm{DL}$ correspondence not only enables gravitational modeling of strongly correlated systems, but also sheds light on a hidden mechanism of the emerging space in both AdS and DL.

TASI lectures on AdS/CFT

Abstract: We introduce the AdS/CFT correspondence as a natural extension of QFT in a fixed AdS background. We start by reviewing some general concepts of CFT, including the embedding space formalism. We then consider QFT in a fixed AdS background and show that one can define boundary operators that enjoy very similar properties as in a CFT, except for the lack of a stress tensor. Including a dynamical metric in AdS generates a boundary stress tensor and completes the CFT axioms. We also discuss some applications of the bulk geometric intuition to strongly coupled QFT. Finally, we end with a review of the main properties of Mellin amplitudes for CFT correlation functions and their uses in the context of AdS/CFT.

Entanglement Entropy for Singular Surfaces

Abstract: We study entanglement entropy for regions with a singular boundary in higher dimensions using the AdS/CFT correspondence and find that various singularities make new universal contributions. When the boundary CFT has an even spacetime dimension, we find that the entanglement entropy of a conical surface contains a term quadratic in the logarithm of the UV cut-off. In four dimensions, the coefficient of this contribution is proportional to the central charge c. A conical singularity in an odd number of spacetime dimensions contributes a term proportional to the logarithm of the UV cut-off. We also study the entanglement entropy for various boundary surfaces with extended singulari- ties. In these cases, similar universal terms may appear depending on the dimension and curvature of the singular locus.

On the universal identity in second order hydrodynamics

Abstract: We compute the ’t Hooft coupling correction to the infinite coupling expression for the second order transport coefficient λ 2 in $$ \mathcal{N}=4 $$ SU(N c ) supersymmetric Yang-Mills theory at finite temperature in the limit of infinite N c , which originates from the R 4 terms in the low energy effective action of the dual type IIB string theory. Using this result, we show that the identity involving the three second order transport coefficients, 2ητ Π − 4λ 1 − λ 2 = 0, previously shown by Haack and Yarom to hold universally in relativistic conformal field theories with string dual descriptions to leading order in supergravity approximation, holds also at next to leading order in this theory. We also compute corrections to transport coefficients in a (hypothetical) strongly interacting conformal fluid arising from the generic curvature squared terms in the corresponding dual gravity action (in particular, Gauss-Bonnet action), and show that the identity holds to linear order in the higher-derivative couplings. We discuss potential implications of these results for the near-equilibrium entropy production rate at strong coupling.

Holographic models of de Sitter QFTs

Abstract: We describe the dynamics of strongly coupled field theories in de Sitter spacetime using the holographic gauge/gravity duality. The main motivation for this is to explore the possibility of dynamical phase transitions during cosmological evolution. Specifically, we study two classes of theories: (i) conformal field theories on de Sitter in the static patch which are maintained in equilibrium at temperatures that may differ from the de Sitter temperature and (ii) confining gauge theories on de Sitter spacetime. In the former case we show that such states make sense from the holographic viewpoint in that they have regular bulk gravity solutions. In the latter situation we add to the evidence for a confinement/deconfinement transition for a large N planar gauge theory as the cosmological acceleration is increased past a critical value. For the field theories we study, the critical acceleration corresponds to a de Sitter temperature which is less than the Minkowski space deconfinement transition temperature by a factor of the spacetime dimension.