Supersymetry on the Noncommutative Lattice

TL;DR

This paper develops a method to construct supersymmetric noncommutative lattice gauge theories, demonstrating how to preserve supersymmetry through orbifold conditions and analyzing the effects of a deformation parameter on supersymmetry enhancement.

Contribution

It introduces a detailed prescription for implementing supersymmetric noncommutative lattice gauge theories using orbifold conditions, including a novel deformation parameter affecting supersymmetry.

Findings

Supersymmetry is preserved on the lattice via orbifold conditions.

A complex deformation parameter influences the continuum limit behavior.

Supersymmetry enhancement occurs only at a specific deformation value.

Abstract

Built upon the proposal of Kaplan et.al. [hep-lat/0206109], we construct noncommutative lattice gauge theory with manifest supersymmetry. We show that such theory is naturally implementable via orbifold conditions generalizing those used by Kaplan {\sl et.al.} We present the prescription in detail and illustrate it for noncommutative gauge theories latticized partially in two dimensions. We point out a deformation freedom in the defining theory by a complex-parameter, reminiscent of discrete torsion in string theory. We show that, in the continuum limit, the supersymmetry is enhanced only at a particular value of the deformation parameter, determined solely by the size of the noncommutativity.