Adjoint Fermion Matrix Models

TL;DR

This paper analyzes fermionic matrix models, deriving exact large-N solutions for one-matrix, two-matrix, and higher-dimensional cases, revealing their universality classes and explicit solutions for quadratic potentials.

Contribution

It introduces a comprehensive method to solve fermionic matrix models at large N, including explicit solutions and universality class identification.

Findings

Large-N solutions derived for fermionic matrix models.

Fermionic one-matrix model shares universality with Hermitean models.

Explicit solutions obtained for quadratic potentials in multi-matrix models.

Abstract

We study fermionic one-matrix, two-matrix and $D$-dimensional gauge invariant matrix models. In all cases we derive loop equations which unambiguously determine the large-$N$ solution. For the one-matrix case the solution is obtained for an arbitrary interaction potential and turns out to be equivalent to the one for the Hermitean one-matrix model with a logarithmic potential and, therefore, belongs to the same universality class. The explicit solutions for the fermionic two-matrix and $D$-dimensional matrix models are obtained at large $N$ (or in the spherical approximation) for the quadratic potential.