Holographic entanglement for Chern-Simons terms

We derive the holographic entanglement entropy contribution from pure and mixed gravitational Chern-Simons(CS) terms in AdS2k+1. This is done through two different methods: first, by a direct evaluation of CS action in a holographic replica geometry and second by a descent of Dong’s derivation applied to the corresponding anomaly polynomial. In lower dimensions (k = 1, 2), the formula coincides with the Tachikawa formula for black hole entropy from gravitational CS terms. New extrinsic curvature corrections appear for k ≥ 3: we give explicit and concise expressions for the two pure gravitational CS terms in AdS7 and present various consistency checks, including agreements with the black hole entropy formula when evaluated at the bifurcation surface.