The Effects of the Gravitational Chern-Simons Term in the AdS$_{2+1}$ Geometry

TL;DR

This paper investigates how the gravitational Chern-Simons term influences the properties of black holes and boundary theories in (2+1)-dimensional AdS space, revealing modifications to black hole parameters and boundary chiral theories.

Contribution

It provides new solutions and analysis of the effects of the gravitational Chern-Simons term on black hole parameters and boundary conformal field theories in AdS$_{2+1}$.

Findings

BTZ black hole mass and angular momentum are rescaled by the GCST.

Boundary WZW theory becomes chiral with different Kac-Moody levels.

Entropy matches area law only at large levels and zero GCST limit, but with incorrect coefficient.

Abstract

We study the effect of the gravitational Chern-Simons term (GCST) in the (2+1)-dimensional anti-de Sitter (AdS$_{2+1}$) geometry. In the context of the gauge gravity, we obtain black hole solution and its boundary WZW theory. The BTZ black hole solution can still be retrieved but its gravitational mass and angular momentum become different from their inherent values. The deformation on these quantities due to the GCST can be summarized as $SO(1,1)$ times rescaling. The boundary WZW theory is found to be chiral, i.e., composed of the right moving part and the left moving part with different Kac-Moody levels. The statistical entropy is proportional to the area only for the large levels and vanishing GCST limit, but its coefficient is not the correct order in the Newton constant $G$. Some related physics are discussed.