Entanglement entropy for free scalar fields in AdS

TL;DR

This paper calculates entanglement entropy for free scalar fields in AdS space, deriving exact Renyi entropy expressions and 1-loop corrections, and relates entropy differences to central charge shifts in holographic CFTs.

Contribution

It provides new exact formulas for Renyi entropy in odd-dimensional AdS and evaluates quantum corrections to holographic entanglement entropy.

Findings

Exact Renyi entropy expressions for odd-dimensional AdS

1-loop quantum corrections to holographic entanglement entropy

Entanglement entropy difference proportional to central charge shift

Abstract

We compute entanglement entropy for free massive scalar fields in anti-de Sitter (AdS) space. The entangling surface is a minimal surface whose boundary is a sphere at the boundary of AdS. The entropy can be evaluated from the thermal free energy of the fields on a topological black hole by using the replica method. In odd-dimensional AdS, exact expressions of the Renyi entropy $S_n$ are obtained for arbitrary $n$. We also evaluate 1-loop corrections coming from the scalar fields to holographic entanglement entropy. Applying the results, we compute the leading difference of entanglement entropy between two holographic CFTs related by a renormalization group flow triggered by a double trace deformation. The difference is proportional to the shift of a central charge under the flow.