Noncommutative gauge and gravity theories and geometric Seiberg-Witten map

TL;DR

This paper provides a pedagogical overview of noncommutative gauge and gravity theories using the Seiberg-Witten map, illustrating how noncommutative actions relate to their commutative counterparts with additional interaction terms.

Contribution

It introduces the use of the Seiberg-Witten map to express noncommutative Einstein gravity in terms of commutative fields, clarifying the role of noncommutativity in gravitational theories.

Findings

Expressed noncommutative Einstein gravity via the Seiberg-Witten map.

Demonstrated how noncommutative actions relate to commutative actions with extra interactions.

Provided a pedagogical framework for understanding noncommutative gauge and gravity theories.

Abstract

We give a pedagogical account of noncommutative gauge and gravity theories, where the exterior product between forms is deformed into a $\star$-product via an abelian twist (e.g. the Groenewold-Moyal twist). The Seiberg-Witten map between commutative and noncommutative gauge theories is introduced. It allows to express the action of noncommutative Einstein gravity coupled to spinor fields in terms of the usual commutative action with commutative fields plus extra interaction terms dependent on the noncommutativity parameter.