Entanglement entropy in scalar field theory on the fuzzy sphere

TL;DR

This paper investigates entanglement entropy in scalar field theories on the fuzzy sphere, employing a replica method applicable to both free and interacting fields, and reveals novel behaviors at strong coupling through Monte Carlo simulations.

Contribution

It introduces a replica-based method for calculating entanglement entropy in matrix models on the fuzzy sphere, extending analysis to interacting fields and strong coupling regimes.

Findings

Results for free fields match previous studies, validating the method.

Monte Carlo simulations reveal new entanglement behaviors at strong coupling.

The method is applicable to both free and interacting scalar fields.

Abstract

We study entanglement entropy on the fuzzy sphere. We calculate it in a scalar field theory on the fuzzy sphere, which is given by a matrix model. We use a method that is based on the replica method and applicable to interacting fields as well as free fields. For free fields, we obtain the results consistent with the previous study, which serves as a test of the validity of the method. For interacting fields, we perform Monte Carlo simulations at strong coupling and see a novel behavior of entanglement entropy.