Renormalization of Entanglement Entropy from topological terms

TL;DR

This paper introduces a new renormalization scheme for entanglement entropy in 3D conformal field theories with gravity duals, using topological boundary terms to cancel divergences.

Contribution

It proposes adding the Chern form as a boundary term in the holographic entanglement entropy calculation to achieve renormalization.

Findings

The boundary term cancels the divergent part of the entropy.

The scheme aligns with topological renormalization in AdS gravity.

It reproduces known results by Taylor and Woodhead.

Abstract

We propose a renormalization scheme for Entanglement Entropy of 3D CFTs with a 4D asymptotically AdS gravity dual in the context of the gauge/gravity correspondence. The procedure consists in adding the Chern form as a boundary term to the area functional of the Ryu-Takayanagi minimal surface. We provide an explicit prescription for the renormalized Entanglement Entropy, which is derived via the replica trick. This is achieved by considering a Euclidean gravitational action renormalized by the addition of the Chern form at the spacetime boundary, evaluated in the conically-singular replica manifold. We show that the addition of this boundary term cancels the divergent part of the Entanglement Entropy, recovering the results obtained by Taylor and Woodhead. We comment on how this prescription for renormalizing the Entanglement Entropy is in line with the general program of topological renormalization in asymptotically AdS gravity.