Noncommutative Theories, Seiberg-Witten Map and Gravity

TL;DR

This paper reviews how noncommutative field theories relate to gravity, showing that noncommutativity induces a charge-dependent gravitational background and affects dispersion relations.

Contribution

It demonstrates the use of the Seiberg-Witten map to interpret noncommutative effects as a charge-dependent gravitational background.

Findings

Noncommutativity mimics a gravitational plane wave background.

Uncharged fields couple more strongly than charged fields.

Dispersion relations are charge-dependent.

Abstract

We review the connection between noncommutative field theories and gravity. When the noncommutativity is induced by the Moyal product we can use the Seiberg-Witten map in order to deal with ordinary fields. We then show that the effect of the noncommutativity is the same as a field dependent gravitational background. The gravitational background is that of a gravitational plane wave and the coupling is charge dependent. Uncharged fields couple more strongly than the charged ones. Deviations from the usual dispersion relations are discussed and we show that they are also charge dependent.