We conjecture a universal formula for the heat current of a steady state connecting two asymptotic equilibrium systems in d-dimensional conformal field theories. Our proposal is verified by comparing it to exact expressions in 1+1 dimensions and linear hydrodynamics as well as numerical simulations in an Israel-Stewart like theory of second order viscous hydrodynamics.

We give a prescription for calculating the entanglement entropy in holographic probe brane systems by systematically taking the leading order backreaction of the probe brane into account. We find a simple compact double integral formula, which is insensitive to many details of the backreaction, most notably the internal space or the non-metric fields sourced by the probe. We validate our method by comparing to exact results in solvable toy models. We also determine the entanglement entropies for a sphere and a strip in the top-down D3/D7 and D3/D5 system. For the sphere the entanglement entropy has also been obtained by other methods and we find perfect agreement.

In this article we present a novel set of solutions of the probe brane system consisting of N f -D5 probe branes embedded in the near-horizon geometry generated by N c -D3 branes, with the D5 worldvolume U (1) gauge fields turned on. Our system is holographically dual to a supersymmetric defect field theory at finite density in non-trivial vacua. We find that a large class of vacua turns out to satisfy a no-force condition, even with supersymmetry explicitly broken by the finite density; our solutions include configuration in which charge separates from the horizon and is instead carried by probe branes outside the horizon. The free energy is lowered in this process. Whether this corresponds to a genuine instability of the finite-density probe brane system remains to be seen.

Abstract:We study Abelian Maxwell-Chern-Simons theory in three-dimensional AdS black hole backgrounds for both integer and non-integer Chern-Simons coupling. Such theories can be derived from various string theory constructions, which we review in the present work. In particular we find exact solutions in the low frequency, low momentum limit, ω, k T (hydrodynamic limit). Using the holographic principle, we translate our results into correlation functions of vector and scalar operators in the dual strongly coupled 1+1-dimensional quantum field theory with a chiral anomaly at non-zero temperature T . Starting from the conformal case we show applicability of the hydrodynamic limit and discuss extensions to the non-conformal case. Correlation functions in the conformal case are compared to an exact field theoretic computation.