Non-commutativity and Supersymmetry

TL;DR

This paper investigates how abelian Yang-Mills gauge symmetry can be deformed by a two-form scale while preserving supersymmetry, concluding that the star product deformation is essentially unique.

Contribution

It demonstrates that the only deformation compatible with both the two-form scale and supersymmetry is the star product, and analyzes the supersymmetry algebra in non-commutative Yang-Mills.

Findings

Star product is the unique deformation under given conditions.

Supersymmetry algebra in NCYM has non-gauge-invariant supercharges.

Action remains quadratic in fermions to all orders in theta.

Abstract

We study the extent to which the gauge symmetry of abelian Yang-Mills can be deformed under two conditions: first, that the deformation depend on a two-form scale. Second, that the deformation preserve supersymmetry. We show that (up to a single parameter) the only allowed deformation is the one determined by the star product. We then consider the supersymmetry algebra satisfied by NCYM expressed in commutative variables. The algebra is peculiar since the supercharges are not gauge-invariant. However, the action, expressed in commutative variables, appears to be quadratic in fermions to all orders in theta.