Renormalized holographic entanglement entropy in Lovelock gravity

TL;DR

This paper introduces a new non-perturbative renormalization method for holographic entanglement entropy in Lovelock gravity, improving divergence cancellation and enabling the identification of C-function candidates in dual CFTs.

Contribution

It proposes a Kounterterm-based renormalization prescription for the Jacobson-Myers functional in Lovelock gravity, enhancing divergence removal without requiring Einstein limit behavior.

Findings

Successful divergence cancellation up to next-to-leading order

Explicit construction of C-function candidates for dual CFTs

Demonstration of the non-perturbative advantage of the Kounterterm method

Abstract

We study the renormalization of Entanglement Entropy in holographic CFTs dual to Lovelock gravity. It is known that the holographic EE in Lovelock gravity is given by the Jacobson-Myers (JM) functional. As usual, due to the divergent Weyl factor in the Fefferman-Graham expansion of the boundary metric for Asymptotically AdS spaces, this entropy functional is infinite. By considering the Kounterterm renormalization procedure, which utilizes extrinsic boundary counterterms in order to renormalize the on-shell Lovelock gravity action for AAdS spacetimes, we propose a new renormalization prescription for the Jacobson-Myers functional. We then explicitly show the cancellation of divergences in the EE up to next-to-leading order in the holographic radial coordinate, for the case of spherical entangling surfaces. Using this new renormalization prescription, we directly find the $C-$function candidates for odd and even dimensional CFTs dual to Lovelock gravity. Our results illustrate the notable improvement that the Kounterterm method affords over other approaches, as it is non-perturbative and does not require that the Lovelock theory has limiting Einstein behavior.