Holography with Gravitational Chern-Simons Term

TL;DR

This paper investigates the effects of a gravitational Chern-Simons term on holography, revealing modifications to stress-energy tensors, anomalies, and black hole entropy, with consistency shown via boundary CFT calculations.

Contribution

It introduces a method to incorporate the gravitational Chern-Simons term into holographic analysis, detailing its impact on anomalies and black hole entropy calculations.

Findings

The stress-energy tensor exhibits conformal and gravitational anomalies.

Black hole entropy is modified by the Chern-Simons term, especially for the BTZ black hole.

Boundary CFT calculations using the Cardy formula match the modified entropy.

Abstract

The holographic description in the presence of gravitational Chern-Simons term is studied. The modified gravitational equations are integrated by using the Fefferman-Graham expansion and the holographic stress-energy tensor is identified. The stress-energy tensor has both conformal anomaly and gravitational or, if re-formulated in terms of the zweibein, Lorentz anomaly. We comment on the structure of anomalies in two dimensions and show that the two-dimensional stress-energy tensor can be reproduced by integrating the conformal and gravitational anomalies. We study the black hole entropy in theories with a gravitational Chern-Simons term and find that the usual Bekenstein-Hawking entropy is modified. For the BTZ black hole the modification is determined by area of the inner horizon. We show that the total entropy of the BTZ black hole is precisely reproduced in a boundary CFT calculation using the Cardy formula.