Mass Deformations of Super Yang-Mills Theories in D= 2+1, and Super-Membranes: A Note

TL;DR

This paper explores mass deformations in 3D supersymmetric Yang-Mills theories, showing how they produce massive matrix quantum mechanics models through dimensional reduction, and providing explicit action formulas.

Contribution

It demonstrates that known massive matrix models originate from mass-deformed 3D super Yang-Mills theories via dimensional reduction.

Findings

Massive spectra are obtained in reduced matrix models.

Mass deformations lead to known quantum mechanical models.

Explicit formulas for gauge theory actions are provided.

Abstract

Mass deformations of supersymmetric Yang-Mills theories in three spacetime dimensions are considered. The gluons of the theories are made massive by the inclusion of a non-local gauge and Poincare invariant mass term due to Alexanian and Nair, while the matter fields are given standard Gaussian mass-terms. It is shown that the dimensional reduction of such mass deformed gauge theories defined on $R^3$ or $R\times T^2$ produces matrix quantum mechanics with massive spectra. In particular, all known massive matrix quantum mechanical models obtained by the deformations of dimensional reductions of minimal super Yang-Mills theories in diverse dimensions are shown also to arise from the dimensional reductions of appropriate massive Yang-Mills theories in three spacetime dimensions. Explicit formulae for the gauge theory actions are provided.