MASS DEFORMATIONS OF SUPER YANG–MILLS THEORIES IN D = 2 + 1, AND SUPER-MEMBRANES: A NOTE

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 nonlocal gauge and Poincaré 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 R3 or R × T2 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 formulas for the gauge theory actions are provided.