Effects of a fundamental mass term in two-dimensional super Yang-Mills theory

TL;DR

This paper investigates how adding a vacuum expectation value to a gauge field in two-dimensional super Yang-Mills theory generates mass terms for fundamental fields while preserving supersymmetry, analyzing the spectrum and bound state properties.

Contribution

It demonstrates that a fundamental mass term can be introduced via a vacuum expectation value without breaking supersymmetry, extending understanding of mass generation in 2D super Yang-Mills.

Findings

Existence of at least one massless state when Chern-Simons coupling is zero

Spectrum separates into light and heavy states as Chern-Simons coupling increases

Evidence suggests the mass gap persists in the continuum limit

Abstract

We show that adding a vacuum expectation value to a gauge field left over from a dimensional reduction of three-dimensional pure supersymmetric Yang-Mills theory generates mass terms for the fundamental fields in the two-dimensional theory while supersymmetry stays intact. This is similar to the adjoint mass term that is generated by a Chern-Simons term in this theory. We study the spectrum of the two-dimensional theory as a function of the vacuum expectation value and of the Chern-Simons coupling. Apart from some symmetry issues a straightforward picture arises. We show that at least one massless state exists if the Chern-Simons coupling vanishes. The numerical spectrum separates into (almost) massless and very heavy states as the Chern-Simons coupling grows. We present evidence that the gap survives the continuum limit. We display structure functions and other properties of some of the bound states.