Twisted Gauge and Gravity Theories on the Groenewold-Moyal Plane

TL;DR

This paper develops a framework for formulating gauge and gravity theories on the Groenewold-Moyal plane using twisted symmetries, ensuring gauge invariance and consistency with noncommutative geometry, and explores the implications for quantum field interactions.

Contribution

It introduces a new approach to noncommutative gauge and gravity theories based on twisted symmetries, allowing arbitrary gauge groups and consistent interactions without additional gauge fields.

Findings

Classical gravity and gauge sectors remain unchanged at theta=0.

Interactions with matter fields depend on the noncommutativity parameter theta.

The approach enables quantum gauge theories with arbitrary gauge groups on the noncommutative plane.

Abstract

Recent work [hep-th/0504183,hep-th/0508002] indicates an approach to the formulation of diffeomorphism invariant quantum field theories (qft's) on the Groenewold-Moyal (GM) plane. In this approach to the qft's, statistics gets twisted and the S-matrix in the non-gauge qft's becomes independent of the noncommutativity parameter theta^{\mu\nu}. Here we show that the noncommutative algebra has a commutative spacetime algebra as a substructure: the Poincare, diffeomorphism and gauge groups are based on this algebra in the twisted approach as is known already from the earlier work of [hep-th/0510059]. It is natural to base covariant derivatives for gauge and gravity fields as well on this algebra. Such an approach will in particular introduce no additional gauge fields as compared to the commutative case and also enable us to treat any gauge group (and not just U(N)). Then classical gravity and gauge sectors are the same as those for \theta^{\mu \nu}=0, but their interactions with matter fields are sensitive to theta^{\mu \nu}. We construct quantum noncommutative gauge theories (for arbitrary gauge groups) by requiring consistency of twisted statistics and gauge invariance. In a subsequent paper (whose results are summarized here), the locality and Lorentz invariance properties of the S-matrices of these theories will be analyzed, and new non-trivial effects coming from noncommutativity will be elaborated. This paper contains further developments of [hep-th/0608138] and a new formulation based on its approach.