Holographic entanglement chemistry

TL;DR

The paper develops an extended first law of entanglement by applying the Iyer-Wald formalism to diffeomorphism-invariant gravities with varying couplings $\Lambda$, $G$, and higher-derivative terms. By analyzing Einstein, Gauss-Bonnet, and Lovelock theories, it derives explicit conjugate quantities to each coupling and expresses the extended law in terms of entanglement entropy $S_{EE}$, modular energy $\delta E$, and central charges such as $c$ or $a_d^*$, thereby connecting boundary entanglement to bulk coupling variations and RG flows. The results show that, in higher-derivative theories, the extra variations organize into central charges, highlighting an RG-analytic structure in the space of dual field theories. These findings link entanglement thermodynamics to black hole chemistry and offer a framework to infer bulk couplings and phase structure from holographic entanglement data. Implications include potential new probes of RG flows and $c$-theorems in higher dimensions and a deeper understanding of how boundary data encodes bulk coupling dynamics.

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 $Λ$ 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.