Holographic entanglement chemistry

TL;DR

This paper extends the first law of entanglement to include variations in fundamental constants and couplings, linking gravitational parameters to dual field theory properties and exploring implications for RG flows and c-theorems.

Contribution

It derives an extended first law of entanglement incorporating variations in cosmological and gravitational couplings for Einstein, Gauss-Bonnet, and Lovelock gravities.

Findings

Extended first law includes variations in $\Lambda$, $G$, and couplings.

Reorganization of variations in terms of central charges.

Implications for RG flows and c-theorems in higher dimensions.

Abstract

We use the Iyer-Wald formalism to derive an extended first law of entanglement that includes variations in the cosmological constant, Newton's constant and --in the case of higher-derivative theories-- all the additional couplings of the theory. In Einstein gravity, where the number of degrees of freedom $N^2$ of the dual field theory is a function of $\Lambda$ and $G$, our approach allows us to vary $N$ keeping the field theory scale fixed or to vary the field theory scale keeping $N$ fixed. We also derive an extended first law of entanglement for Gauss-Bonnet and Lovelock gravity and show that in these cases all the extra variations reorganize nicely in terms of the central charges of the theory. Finally, we comment on the implications for renormalization group flows and c-theorems in higher dimensions.