Arbitrary rotation invariant random matrix ensembles and supersymmetry: orthogonal and unitary-symplectic case

TL;DR

This paper extends the supersymmetry method to include arbitrary orthogonally and unitary-symplectically invariant random matrix ensembles, providing explicit formulas and discussing correlation features.

Contribution

It completes the extension of the supersymmetry approach to more general matrix ensembles beyond Gaussian cases, using a different method from superbosonization.

Findings

Explicit expressions for one-point functions

Unified formulation of results

Discussion of higher order correlation features

Abstract

Recently, the supersymmetry method was extended from Gaussian ensembles to arbitrary unitarily invariant matrix ensembles by generalizing the Hubbard-Stratonovich transformation. Here, we complete this extension by including arbitrary orthogonally and unitary-symplectically invariant matrix ensembles. The results are equivalent to, but the approach is different from the superbosonization formula. We express our results in a unifying way. We also give explicit expressions for all one-point functions and discuss features of the higher order correlations.