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

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.