Holographic Gravitational Anomaly and Chiral Vortical Effect

TL;DR

This paper presents a holographic, bottom-up five-dimensional model that encapsulates the mixed gauge–gravitational anomaly through a Chern–Simons term and analyzes its impact on anomalous transport. Using holographic renormalization and Kubo formulas, the authors compute the chiral magnetic and chiral vortical conductivities in a charged AdS black hole background, finding a $T^2$ contribution from the gravitational anomaly that remains unrenormalized at strong coupling. The results align with weak-coupling predictions, supporting a non-renormalization of the anomalous conductivities and confirming that the holographic setup reproduces the correct anomaly structure without introducing new UV divergences. The work lays groundwork for extending to non‑abelian cases and for connecting to hydrodynamic constitutive relations via fluid/gravity methods.

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.