Fortuity with a single matrix

TL;DR

This paper introduces an exactly solvable supersymmetric quantum mechanical model with a single $U(N)$ adjoint fermionic matrix, exploring special states at finite and large $N$ using matrix integrals.

Contribution

It constructs a novel supersymmetric matrix model and develops a method to analyze its behavior as the matrix size $N$ varies, especially in the large $N$ limit.

Findings

Identification of special fortuitous states in the model

Development of a technique to track $N$ in matrix integrals

Insights into the sensitivity of matrix integral solutions to $N$

Abstract

We construct and study a supersymmetric quantum mechanical model with a single $U(N)$ adjoint fermionic matrix. The model is exactly solvable yet contains a large number of fortuitous states. We investigate these states exactly at finite $N$ and, in the large $N$ limit, via a unitary matrix model. In particular, we develop a way to "follow $N$" in the unitary matrix integral and study how the answer of the integral depends sensitively on the value of $N$.