Equivariant Localization in Stochastic Quantization and Quenched Matrix Models

TL;DR

This paper reveals that stochastic quantization's supersymmetry aligns with equivariant cohomology, applying localization principles to establish equivalences between matrix models and their quenched versions.

Contribution

It demonstrates the equivariant cohomological structure of stochastic quantization and applies localization to connect matrix models with quenched Eguchi-Kawai models.

Findings

Supersymmetry in stochastic quantization is a Cartan model of equivariant cohomology.

Localization principles establish equivalence between matrix models and quenched models.

The approach unifies supersymmetry, cohomology, and matrix model analysis.

Abstract

It is shown that Parisi-Sourlas supersymmetry of stochastic quantization is a Cartan model of equivariant cohomology. Equivariant cohomological structure of stochastic quantization of linear and non-linear sigma models are discussed. Witten's nonabelian localization principle is applied to the stochastic quantization of matrix models. As a result the equivalence between the original matrix model and the corresponding quenched Eguchi-Kawai model is established.