Extended First Law for Entanglement Entropy in Lovelock Gravity

TL;DR

This paper extends the first law of holographic entanglement entropy in Lovelock gravity to include variations of bulk coupling constants, linking them to changes in boundary CFT degrees of freedom and trace anomaly coefficients.

Contribution

It introduces a generalized first law incorporating bulk Lovelock coupling variations, connecting them to boundary CFT anomalies and degrees of freedom.

Findings

Derived the extended first law including coupling variations.

Linked bulk Lovelock parameters to boundary trace anomalies.

Identified a chemical potential related to entanglement entropy per degree of freedom.

Abstract

The first law for the holographic entanglement entropy of spheres in a boundary CFT with a bulk Lovelock dual is extended to include variations of the bulk Lovelock coupling constants. Such variations in the bulk correspond to perturbations within a family of boundary CFTs. The new contribution to the first law is found to be the product of the variation $\delta a$ of the A-type trace anomaly coefficient for even dimensional CFTs, or more generally its extension $\delta a^*$ to include odd dimensional boundaries, times the ratio $S/a^*$. Since $a^*$ is a measure of the number of degrees of freedom $N$ per unit volume of the boundary CFT, this new term has the form $\mu\delta N$, where the chemical potential $\mu$ is given by the entanglement entropy per degree of freedom.