Holography with a gravitational Chern-Simons term

The holographic description in the presence of the 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 reformulated 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 Banados-Teitelboim-Zanelli (BTZ) black hole, the modification is determined by the area of the inner horizon. We show that the total entropy of the BTZ black hole is precisely reproduced in a boundary conformal field theory calculation using the Cardy formula.