Hydrodynamics in 1+1 dimensions from Maxwell-Chern-Simons theory in AdS_3

TL;DR

This paper explores the hydrodynamic behavior of Abelian Maxwell-Chern-Simons theory in AdS_3 black brane backgrounds, deriving exact solutions and correlation functions relevant to 1+1-dimensional quantum field theories with chiral anomalies.

Contribution

It provides exact solutions in the hydrodynamic limit for Maxwell-Chern-Simons theory in AdS_3 and connects these to correlation functions in dual quantum field theories with anomalies.

Findings

Derived exact solutions in the low frequency, low momentum limit.

Computed holographic correlation functions for vector operators.

Compared holographic results with field theoretic computations.

Abstract

In this presentation we review our work on Abelian Maxwell-Chern-Simons theory in three-dimensional AdS black brane backgrounds, with both integer and non-integer Chern-Simons coupling. Such theories can be derived from several string theory constructions, and we found exact solutions in the low frequency, low momentum limit (omega, k << T, the hydrodynamic limit). Our results are translated into correlation functions of vector operators in the dual strongly coupled 1+1-dimensional quantum field theory with a chiral anomaly at non-zero temperature T, via the holographic correspondence. The applicability of the hydrodynamic limit is discussed, together with the comparison between an exact field theoretic computation and the found holographic correlation functions in the conformal case.