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. © 2009 Elsevier B.V. All rights reserved.
Hotta, K., Hyakutake, Y., Kubota, T., Nishinaka, T., & Tanida, H. (2009). Left-right asymmetric holographic RG flow with gravitational Chern-Simons term. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 680(3), 279–285. https://doi.org/10.1016/j.physletb.2009.08.060