Holography with Gravitational Chern-Simons Term

TL;DR

The paper analyzes holography in AdS3 when a gravitational Chern-Simons term is present, showing it induces a gravitational (Lorentz) anomaly in the boundary CFT while leaving the conformal anomaly intact. Using a Fefferman-Graham expansion, it derives the modified holographic stress-energy tensor and its anomalous Ward identities, and demonstrates a precise boundary-bulk match for BTZ black hole entropy through the Cardy formula, with central charges c_L and c_R depending on the CS coupling β. It also reveals a striking feature: in CS-dominated gravity, the black hole entropy becomes sensitive to the inner horizon area r_- rather than the outer horizon, offering new insights into the microscopic origin of entropy and the role of interior horizon data in holography. The work further discusses how 2D anomalies can be organized via boundary counterterms and how the M, J shifts in the bulk reflect the boundary CFT structure, establishing a consistent holographic picture for topologically massive gravity. Overall, it extends AdS3/CFT2 to include gravitational anomalies and topological mass, linking geometric bulk features to boundary central charges and entropy in a novel way.

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.