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.

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.