Left-Right Asymmetric Holographic RG Flow with Gravitational Chern-Simons Term

TL;DR

This paper investigates holographic RG flows in 3D gravity with a gravitational Chern-Simons term, deriving flow equations for anomalies and c-functions that reflect parity violation and are consistent with the c-theorem.

Contribution

It introduces a Hamilton-Jacobi approach to analyze RG flows with gravitational Chern-Simons terms, deriving monotonic c-functions for left and right movers.

Findings

Flow equations for Weyl and gravitational anomalies obtained.

Left and right moving c-functions are monotonic along the flow.

The difference between c-functions is linked to the Chern-Simons coefficient.

Abstract

We consider the holographic renormalization group (RG) flow in three dimensional gravity with the gravitational Chern-Simons term coupled to some scalar fields. We apply the canonical approach to this higher derivative case and employ the Hamilton-Jacobi formalism to analyze the flow equations of two dimensional field theory. Especially we obtain flow equations of Weyl and gravitational anomalies, and derive $c$-functions for left and right moving modes. Both of them are monotonically non-increasing along the flow, and the difference between them is determined by the coefficient of the gravitational Chern-Simons term. This is completely consistent with the Zamolodchikov's $c$-theorem for parity-violating two-dimensional quantum field theories.