Nonabelian Localization for Statistical Mechanics of Matrix Models at High Temperatures

TL;DR

This paper demonstrates that at high temperatures, the partition function of matrix models localizes on specific phase space shells where matrix variables follow canonical commutation relations, using nonabelian equivariant localization.

Contribution

It introduces a novel application of nonabelian equivariant localization to analyze the high-temperature behavior of matrix models in statistical mechanics.

Findings

Partition function localizes on shells with canonical commutation relations.

Localization is achieved via a nonabelian equivariant localization principle.

Results connect classical phase space structures with quantum-like relations.

Abstract

We show that in the high temperature limit the partition function of a matrix model is localized on certain shells in the phase space where on each shell the classically conjugate matrix variables obey the canonical commutation relations. The result is obtained by applying the nonabelian equivariant localization principle to the partition function of a matrix model driven by a specific random external source coupled to a conserved charge of the system.