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.

Exact higher-spin symmetry in CFT: all correlators in unbroken Vasiliev theory

Abstract: All correlation functions of conserved currents of the CFT that is dual to unbroken Vasiliev theory are found as invariants of higher-spin symmetry in the bulk of AdS. The conformal and higher-spin symmetry of the correlators as well as the conservation of currents are manifest, which also provides a direct link between the Maldacena-Zhiboedov result and higher-spin symmetries. Our method is in the spirit of AdS/CFT, though we never take any boundary limit or compute any bulk integrals. Boundary-to-bulk propagators are shown to exhibit an algebraic structure, living at the boundary of SpH(4), semidirect product of Sp(4) and the Heisenberg group. N-point correlation function is given by a product of N elements.

Anomalies and time reversal invariance in relativistic hydrodynamics: the second order and higher dimensional formulations

Abstract: We present two new results on relativistic hydrodynamics with anomalies and external electromagnetic fields, “Chiral MagnetoHydroDynamics” (CMHD). First, we study CMHD in four dimensions at second order in the derivative expansion assuming the conformal/Weyl invariance. We classify all possible independent conformal second order viscous corrections to the energy-momentum tensor and to the U(1) current in the presence of external electric and/or magnetic fields, and identify eighteen terms that originate from the triangle anomaly. We then propose and motivate the following guiding principle to constrain the CMHD: the anomaly–induced terms that are even under the time reversal invariance should not contribute to the local entropy production rate. This allows us to fix thirteen out of the eighteen transport coefficients that enter the second order formulation of CMHD. We also relate one of our second order transport coefficients to the chiral shear waves. Our second subject is hydrodynamics with (N + 1)-gon anomaly in an arbitrary 2N dimensions. The effects from the (N + 1)-gon anomaly appear in hydrodynamics at (N − 1)’th order in the derivative expansion, and we identify precisely N such corrections to the U(1) current. The time reversal constraint is powerful enough to allow us to find the analytic expressions for all transport coefficients. We confirm the validity of our results (and of the proposed guiding principle) by an explicit fluid/gravity computation within the AdS/CFT correspondence.

Holographic quantum liquid.

Abstract: Quantum liquids are characterized by the distinctive properties such as the low-temperature behavior of heat capacity and the spectrum of low-energy quasiparticle excitations. In particular, at low temperature, Fermi liquids exhibit the zero sound, predicted by Landau in 1957 and subsequently observed in liquid He-3. In this Letter, we ask whether such characteristic behavior is present in theories with a holographically dual description. We consider a class of gauge theories with fundamental matter fields whose holographic dual in the appropriate limit is given in terms of the Dirac-Born-Infeld action in anti-de Sitter space. We find that these systems also exhibit a sound mode at zero temperature despite having a non-Fermi-liquid behavior of the specific heat. These properties suggest that holography identifies a new type of quantum liquid which potentially could be experimentally realized in strongly correlated systems.

Dynamics of Entanglement Entropy from Einstein Equation

Abstract: We study the dynamics of entanglement entropy for weakly excited states in conformal field theories by using anti-de Sitter/conformal field theory (AdS/CFT). This is aimed at a first step to finding a counterpart of the Einstein equation in CFT language. In particular, we point out that the entanglement entropy satisfies differential equations that directly correspond to the Einstein equation in several setups of AdS/CFT. We also define a quantity called entanglement density in higher dimensional field theories and study its dynamical property for weakly excited states in conformal field theories.