# Entanglement entropy of ${\cal N}=2^*$ de Sitter vacuum

## TL;DR

This paper uses holography to compute the entanglement entropy of the de Sitter vacuum in a nonconformal gauge theory, revealing it is distinct from thermodynamic and particle production entropies.

## Contribution

It provides the first holographic calculation of vacuum entanglement entropy in the nonconformal ${
m N}=2^*$ gauge theory on de Sitter space, including exact results via localization.

## Key findings

- Entanglement entropy density is computed for various masses and couplings.
- The entropy is shown to be different from thermodynamic and particle production entropies.
- Exact solutions are obtained for specific curvature couplings using localization.

## Abstract

de Sitter vacuum of nonconformal gauge theories is non-equilibrium, manifested by a nonvanishing rate of the comoving entropy production at asymptotically late times. This entropy production rate is related to the entanglement entropy of the de Sitter vacuum of the theory. We use holographic correspondence to compute vacuum entanglement entropy density $s_{ent}$ of mass deformed ${\cal N}=4$ supersymmetric Yang-Mills theory - the ${\cal N}=2^*$ gauge theory - for various values of the masses and the coupling constant to the background space-time curvature. For a particular choice of the curvature coupling, the Euclidean model can be solved exactly using the supersymmetric localization. We show that ${\cal N}=2^*$ de Sitter entanglement entropy is not the thermodynamic entropy of the localization free energy at de Sitter temperature. Neither it is related to the thermal entropy of de Sitter vacuum of pair-produced particles.