Super-Yang-Mills Theory in SIM(1) Superspace

TL;DR

This paper explores how breaking Lorentz symmetry to SIM(1) in three-dimensional supersymmetric Yang-Mills theory reduces its supersymmetry from N=1 to N=1/2, a novel result without boundary effects.

Contribution

It demonstrates for the first time in three dimensions that Lorentz symmetry breaking to SIM(1) reduces supersymmetry from N=1 to N=1/2 in a boundary-less manifold.

Findings

Supersymmetry is reduced from N=1 to N=1/2 in SIM(1) superspace.

Breaking Lorentz symmetry affects the supersymmetry structure.

First demonstration of such supersymmetry breaking in three dimensions without boundaries.

Abstract

In this paper, we will analyse three dimensional supersymmetric Yang-Mills theory coupled to matter fields in $SIM(1)$ superspace formalism. The original theory which is invariant under the full Lorentz group has $\mathcal{N} =1$ supersymmetry. However, when we break the Lorentz symmetry down to $SIM(1)$ group, the $SIM(1)$ superspace will break half the supersymmetry of the original theory. Thus, the resultant theory in $SIM(1)$ superspace will have $\mathcal{N} =1/2$ supersymmetry. This is the first time that $\mathcal{N} =1 $ supersymmetry will be broken down to $\mathcal{N} =1/2$ supersymmetry, for a three dimensional theory, on a manifold without a boundary. This is because it is not possible to use non-anticommutativity to break $\mathcal{N} =1$ supersymmetry down to $\mathcal{N} =1/2$ supersymmetry in three dimensions.