On the Space-Time Symmetries of Non-Commutative Gauge Theories

TL;DR

This paper investigates the space-time symmetries of non-commutative U(1) gauge theories, concluding that the non-commutativity parameter remains invariant under all transformations except translations, which are symmetries.

Contribution

It provides a detailed analysis of how the non-commutative parameter behaves under various space-time transformations using Noether charges.

Findings

Non-commutative parameter does not transform under conformal transformations.

The theory is only invariant under space-time translations.

The analysis applies to gauge groups beyond U(1).

Abstract

We study the space-time symmetries and transformation properties of the non-commutative U(1) gauge theory, by using Noether charges. We carry out our analysis by keeping an open view on the possible ways $\theta^{\mu \nu}$ could transform. We conclude that $\theta^{\mu \nu}$ cannot transform under any space-time transformation since the theory is not invariant under the conformal transformations, with the only exception of space-time translations. The same analysis applies to other gauge groups.