Holographic Entanglement for Chern-Simons Terms

Abstract

We derive the holographic entanglement entropy contribution from pure and mixed gravitational Chern-Simons(CS) terms in AdS${}_{2k+1}$. 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 Wald-Tachikawa formula for black hole entropy from gravitational CS terms. New extrinsic curvature corrections appear for $k\ge 3$ : we give explicit and concise expressions for the two pure gravitational CS terms in AdS${}_7$ and present various consistency checks, including agreements with the black hole entropy formula when evaluated at the bifurcation surface.

29 pages + 47 pages of appendices ; v3: Typos corrected, minor corrections and JHEP version

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