Holographic Gravitational Anomaly and Chiral Vortical Effect

TL;DR

This paper explores a holographic model incorporating gauge and gravitational anomalies, analyzing their effects on chiral conductivities and demonstrating the non-renormalization of certain anomaly-induced terms at strong coupling.

Contribution

It introduces a holographic framework with a mixed gauge-gravitational Chern-Simons term, detailing renormalization procedures and computing anomaly-related conductivities at strong coupling.

Findings

The T^2 term in chiral vortical conductivity persists at strong coupling.

The gauge-gravitational Chern-Simons term does not introduce new divergences.

The numerical value of the T^2 term is unchanged from weak to strong coupling.

Abstract

We analyze a holographic model with a pure gauge and a mixed gauge-gravitational Chern-Simons term in the action. These are the holographic implementations of the usual chiral and the mixed gauge-gravitational anomalies in four dimensional field theories with chiral fermions. We discuss the holographic renormalization and show that the gauge-gravitational Chern-Simons term does not induce new divergences. In order to cancel contributions from the extrinsic curvature at a boundary at finite distance a new type of counterterm has to be added however. This counterterm can also serve to make the Dirichlet problem well defined in case the gauge field strength vanishes on the boundary. A charged asymptotically AdS black hole is a solution to the theory and as an application we compute the chiral magnetic and chiral vortical conductivities via Kubo formulas. We find that the characteristic term proportional to T^2 is present also at strong coupling and that its numerical value is not renormalized compared to the weak coupling result.