$k$-Minkowski-deformation of $U(1)$ gauge theory

TL;DR

This paper develops an exact non-commutative deformation of U(1) gauge theory on kappa-Minkowski space, maintaining gauge covariance and exploring the implications of a non-trivial commutative limit related to space-time curvature.

Contribution

It provides an all-orders explicit construction of gauge transformations and field strength in kappa-Minkowski-deformed U(1) gauge theory, including a novel gauge-invariant action with a non-trivial measure.

Findings

Exact all-orders expressions for deformed gauge transformations and field strength.

The deformed Yang-Mills Lagrangian reduces to Maxwell in the commutative limit.

Identification of a non-trivial measure related to space-time curvature.

Abstract

We construct a non-commutative kappa-Minkowski deformation of U(1) gauge theory, following a general approach, recently proposed in JHEP 2008 (2020) 041. We obtain an exact (all orders in the non-commutativity parameter) expression for both the deformed gauge transformations and the deformed field strength, which is covariant under these transformations. The corresponding Yang-Mills Lagrangian is gauge covariant and reproduces the Maxwell Lagrangian in the commutative limit. Gauge invariance of the action functional requires a non-trivial integration measure which, in the commutative limit, does not reduce to the trivial one. We discuss the physical meaning of such a nontrivial commutative limit, relating it to a nontrivial space-time curvature of the undeformed theory. Moreover, we propose a rescaled kappa-Minkowski non-commutative structure, which exhibits a standard flat commutative limit.