A Supersymmetry Preserving Mass-Deformation of N=1 Super Yang-Mills in D=2+1

TL;DR

This paper constructs a supersymmetry-preserving massive non-abelian N=1 Super Yang-Mills theory in 2+1 dimensions using a non-local gauge-invariant mass term, exploring its algebraic structure and dimensional reduction to matrix quantum mechanics.

Contribution

It introduces a novel non-local gauge-invariant mass term for N=1 SYM in 3D that preserves supersymmetry and analyzes its algebraic and dimensional reduction properties.

Findings

Successfully constructs a supersymmetry-preserving mass term for N=1 SYM in 3D.

Shows the supersymmetry algebra as a non-central extension of the Poincare algebra.

Relates the reduced theory to a massive N=2 matrix quantum mechanics.

Abstract

We construct a massive non-abelian N= 1 SYM theory on R^3. This is achieved by using a non-local gauge and Poincare invariant mass term for gluons due to Nair. The underlying supersymmetry algebra is shown to be a non-central extension of the Poincare algebra by the spacetime rotation group so(3). The incorporation of Chern-Simons couplings in the formalism is also presented. The dimensional reduction of the gauge theory and the SUSY algebra is related to a massive N=2 massive matrix quantum mechanics based on euclidean $Clifford_2(R)$.