Left–right asymmetric holographic RG flow with gravitational Chern–Simons term

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.