Superbosonization

TL;DR

This paper provides a constructive proof of the superbosonization formula for invariant random matrix ensembles, extending supersymmetry techniques to analyze spectral correlations across various symmetries.

Contribution

It introduces a new constructive proof of the superbosonization formula applicable to multiple symmetry classes, enhancing tools for studying non-Gaussian random matrices.

Findings

Explicit formulas for orthogonal symmetry case

Potential for analyzing universality in spectral correlations

Framework applicable to non-Gaussian ensembles

Abstract

We give a constructive proof for the superbosonization formula for invariant random matrix ensembles, which is the supersymmetry analog of the theory of Wishart matrices. Formulas are given for unitary, orthogonal and symplectic symmetry, but worked out explicitly only for the orthogonal case. The method promises to become a powerful tool for investigating the universality of spectral correlation functions for a broad class of random matrix ensembles of non-Gaussian type.