Gauge theories on the kappa-Minkowski spacetime

TL;DR

This paper develops gauge theories on kappa-Minkowski spacetime, introducing deformed gauge fields and Lorentz covariance, expanding the understanding of noncommutative gauge theories with explicit first-order Lagrangian formulations.

Contribution

It constructs the first gauge theories on kappa-Minkowski spacetime with deformed Lorentz symmetry using enveloping algebra and Seiberg-Witten formalism.

Findings

Explicit first-order Lagrangians for deformed gauge theories

Introduction of derivative-valued gauge fields with curvature and torsion terms

First example of a gauge theory with deformed Lorentz covariance

Abstract

This study of gauge field theories on kappa-deformed Minkowski spacetime extends previous work on field theories on this example of a noncommutative spacetime. We construct deformed gauge theories for arbitrary compact Lie groups using the concept of enveloping algebra-valued gauge transformations and the Seiberg-Witten formalism. Derivative-valued gauge fields lead to field strength tensors as the sum of curvature- and torsion-like terms. We construct the Lagrangians explicitly to first order in the deformation parameter. This is the first example of a gauge theory that possesses a deformed Lorentz covariance.