Wilson lines and entanglement entropy in higher spin gravity

Abstract

Holographic entanglement entropy provides a direct connection between clas- sical geometry and quantum entanglement; however the usual prescription does not apply to theories of higher spin gravity, where standard notions of geometry are no longer gauge invariant. We present a proposal for the holographic computation of entanglement en- tropy in field theories dual to higher spin theories of gravity in AdS3. These theories have a Chern-Simons description, and our proposal involves a Wilson line in an infinite- dimensional representation of the bulk gauge group. In the case of spin-2 gravity such Wilson lines are the natural coupling of a heavy point particle to gravity and so are equiva- lent to the usual prescription of Ryu and Takayanagi. For higher spin gravity they provide a natural generalization of these ideas. We work out spin-3 gravity in detail, showing that our proposal recovers many expected results and computes thermal entropies of black holes with higher spin charge, finding agreement with previous expressions in the literature. We encounter some peculiarities in the case of non-unitary RG ow backgrounds and outline future generalizations. © SISSA 2013.