Extended gravity theories from dynamical noncommutativity

TL;DR

This paper develops an extended gravity theory incorporating dynamical noncommutativity through a geometric Seiberg-Witten map, resulting in higher derivative corrections to Einstein-Hilbert and scalar actions.

Contribution

It introduces a novel coupling of noncommutative vielbein gravity to scalar fields with a geometric generalization of the Seiberg-Witten map, allowing dynamical noncommutativity.

Findings

Higher derivative corrections organized in powers of ^{AB}

All fields remain ordinary (commutative) despite noncommutative structure

Vectors defining the twist become dynamical through scalar fields

Abstract

In this paper we couple noncommutative (NC) vielbein gravity to scalar fields. Noncommutativity is encoded in a star product between forms, given by an abelian twist (a twist with commuting vector fields). A geometric generalization of the Seiberg-Witten map for abelian twists yields an extended theory of gravity coupled to scalars, where all fields are ordinary (commutative) fields. The vectors defining the twist can be related to the scalar fields and their derivatives, and hence acquire dynamics. Higher derivative corrections to the classical Einstein-Hilbert and Klein-Gordon actions are organized in successive powers of the noncommutativity parameter \theta^{AB}.