On the energy-momentum tensor in non-commutative gauge theories

TL;DR

This paper investigates the energy-momentum tensor in non-commutative gauge theories, demonstrating its equivalence to a commutative version obtained via the Seiberg-Witten map, and discusses related properties.

Contribution

It shows that the stress tensor in non-commutative gauge theories matches that from a commutative theory using the Seiberg-Witten map, clarifying its properties.

Findings

Stress tensor coincides with the commutative theory version

Provides insights into the properties of energy-momentum tensor in non-commutative theories

Discusses implications for coupling to gravitational fields

Abstract

We study the properties of the energy-momentum tensor in non-commutative gauge theories by coupling them to a weak external gravitational field. In particular, we show that the stress tensor of such a theory coincides exactly with that derived from a theory where a Seiberg-Witten map has been implemented (namely, the procedure is commutative). Various other interesting features are also discussed.