Quenched Two Dimensional Supersymmetric Yang-Mills Theory

TL;DR

This paper introduces a quenching method for 2D supersymmetric Yang-Mills theory that simplifies analysis by avoiding ultraviolet cut-offs, leading to an exactly solvable extended model with potential implications for understanding supersymmetric gauge theories.

Contribution

It proposes a novel quenching prescription for 2D supersymmetric Yang-Mills theory and derives an exactly solvable extended model with implications for supersymmetric gauge theories.

Findings

A new quenching prescription eliminates the need for ultraviolet cut-offs.

An extended model with one more complex fermion is exactly solvable.

The solvable model exhibits N=1 supersymmetry as Parisi-Sourlas supersymmetry.

Abstract

By studying the pure Yang-Mills theory on a circle, as well as an adjoint scalar coupled to the gauge field on a circle, we propose a quenching prescription in which the combination of the spatial component of the gauge field and $P$ is treated as a dynamic variable. Averaging over momentum is not necessary, therefore the usual ultraviolet cut-off is eliminated. We then apply this prescription to study the large $N$ two dimensional supersymmetric gauge theory. An one dimensional supersymmetric matrix model is obtained. It is not known whether this model can be solved exactly. However, an extended model with one more complex fermion is exactly solvable, with $N=1$ supersymmetry as Parisi-Sourlas supersymmetry. The exact solvability may have some implications for the $N=1$ quenched model.