# Superbosonization in disorder and chaos: The role of anomalies

## TL;DR

This paper develops a rigorous supermatrix approach for calculating fermionic integrals using supersymmetry, with applications to disordered systems and localization phenomena.

## Contribution

It introduces a supermatrix representation of superfield integrals and specifies contours, extending superbosonization to systems with anomalies and disorder.

## Key findings

- Derived a supermatrix representation for superfield integrals.
- Successfully calculated correlation functions in random matrix models.
- Argued applicability to nonperturbative analysis of disordered systems.

## Abstract

Superbosonization formula aims at rigorously calculating fermionic integrals via employing supersymmetry. We derive such a supermatrix representation of superfield integrals and specify integration contours for the supermatrices. The derivation is essentially based on the supersymmetric generalization of the Itzikson-Zuber integral in the presence of anomalies in the Berezinian and shows how an integral over supervectors is eventually reduced to an integral over commuting variables. The approach is tested by calculating both one and two point correlation functions in a class of random matrix models. It is argued that the approach is capable of producing nonperturbative results in various systems with disorder, including physics of many-body localization, and other situations hosting localization phenomena.