We study Abelian Maxwell-Chern-Simons theory in three-dimensional AdS black hole backgrounds for both integer and non-integer Chern-Simons coupling. 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 confirmed by comparison to an exact field-theoretic computation. Also a top-down string construction is provided as the ultraviolet completion for our Maxwell-Chern-Simons actions.