Supermatrix Models

TL;DR

This paper introduces supermatrix models as an extension of bosonic matrix models, exploring their unique properties through different integration choices and analyzing their perturbative and eigenvalue behaviors.

Contribution

It proposes supermatrix models based on supermatrix integrals, revealing their distinct properties and connections to plasma systems and Hermitian models.

Findings

One integration choice yields perturbative structure similar to Hermitian models.

Another choice results in an eigenvalue reduction described by a one-dimensional plasma.

A stationary point of the supermatrix model is identified.

Abstract

Random matrix models based on an integral over supermatrices are proposed as a natural extension of bosonic matrix models. The subtle nature of superspace integration allows these models to have very different properties from the analogous bosonic models. Two choices of integration slice are investigated. One leads to a perturbative structure which is reminiscent of, and perhaps identical to, the usual Hermitian matrix models. Another leads to an eigenvalue reduction which can be described by a two component plasma in one dimension. A stationary point of the model is described.