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 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 AdS 7 and present various consistency checks, including agreements with the black hole entropy formula when evaluated at the bifurcation surface.1 See also an earlier work [6] toward the proof of Ryu-Takayanagi formula and a criticism of this earlier proof can be found in [7].2 Works preceding Dong dealing with higher derivative actions include [10][11][12][13][14][15][16][17]. For some recent works relevant to the higher-derivative correction to holographic entanglement entropy formula, see [18][19][20][21][22][23][24][25][26][27][28][29][30]. See [28] for a generalization to the case involving derivatives of the Riemann tensor. 9 We would like to thank N. Iqbal and A. C. Wall for correspondence. 10 See Appendix A for a list of geometric quantities evaluated on this background. 11 We note that our notation for the Euclidean action deviates from [8] by a minus sign.

Entropy for gravitational Chern-Simons terms by squashed cone method

“…Our main discussion below is about how to eliminate the ambiguity in the non-covariant theory when using the squashed cone method by Lewkowycz-Maldacena [5] and Dong [8]. Our approach is consistent with the results of [19,35,38].…”

Anomalies and entanglement entropy

“…Some other works on anomalies include [22][23][24][25][26][27]. In this work, we focus our attention on the effect of anomalies on entanglement entropy, previously studied also in [28][29][30][31][32].…”

Universality of anomalous conductivities in theories with higher-derivative holographic duals

“…Lastly, we point out that many recent works have found novel structures in entanglement entropy of theories with anomalies [113][114][115][116][117]. As a result of non-renormalisation, one may expect there to exist strong constraints on the structure of extremal bulk sur- 15 We thank the anonymous JHEP referee for a discussion regarding this point.…”