Noncommutative Field Theories and Gravity

TL;DR

This paper demonstrates that noncommutative field theories, after the Seiberg-Witten map, can be interpreted as ordinary theories coupled to a gauge field-dependent gravitational background, revealing charge-dependent gravitational effects.

Contribution

It shows that noncommutative field theories can be viewed as ordinary theories in a gravitational background generated by the gauge field, with distinct couplings for charged and uncharged fields.

Findings

Uncharged fields couple more strongly to the gravitational background.

The background is a gravitational plane wave.

Massless particles have velocity deviations from light speed depending on charge.

Abstract

We show that after the Seiberg-Witten map is performed the action for noncommutative field theories can be regarded as a coupling to a field dependent gravitational background. This gravitational background depends only on the gauge field. Charged and uncharged fields couple to different backgrounds and we find that uncharged fields couple more strongly than the charged ones. We also show that the background is that of a gravitational plane wave. A massless particle in this background has a velocity which differs from the velocity of light and we find that the deviation is larger in the uncharged case. This shows that noncommutative field theories can be seen as ordinary theories in a gravitational background produced by the gauge field with a charge dependent gravitational coupling.