# Gauged fermionic matrix quantum mechanics

## TL;DR

This paper analyzes a gauged fermionic matrix model in the large N limit, showing that trace and Schur function bases are equivalent up to a normalization, with implications for understanding fermionic systems in 1+1 dimensions.

## Contribution

It proves the equivalence of trace and Schur function bases in the gauged fermionic matrix model, including the explicit normalization factor, advancing the understanding of fermionic gauge theories.

## Key findings

- Trace and Schur bases coincide up to a normalization
- Explicit normalization coefficient computed
- Provides insight into fermionic matrix models in 1+1 dimensions

## Abstract

We consider the gauged free fermionic matrix model, for a single fermionic matrix. In the large $N$ limit this system describes a $c=1/2$ chiral fermion in $1+1$ dimensions. The Gauss' law constraint implies that to obtain a physical state, indices of the fermionic matrices must be fully contracted, to form a singlet. There are two ways in which this can be achieved: one can consider a trace basis formed from products of traces of fermionic matrices or one can consider a Schur function basis, labeled by Young diagrams. The Schur polynomials for the fermions involve a twisted character, as a consequence of Fermi statistics. The main result of this paper is a proof that the trace and Schur bases coincide up to a simple normalization coefficient that we have computed.

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Source: https://tomesphere.com/paper/1903.01628