Gauge theory on kappa-Minkowski revisited: the twist approach

TL;DR

This paper clarifies the geometric structure of gauge transformations on kappa-Minkowski space-time using the twist approach, constructing a consistent action for noncommutative U(1) gauge fields and analyzing first-order corrections.

Contribution

It introduces a geometric framework for gauge transformations on kappa-Minkowski space-time and constructs the first-order corrected action using the Seiberg-Witten map.

Findings

Constructed a geometric action for noncommutative U(1) gauge fields.

Resolved ambiguities in gauge transformation definitions.

Derived first-order deformation corrections using Seiberg-Witten map.

Abstract

Kappa-Minkowski space-time is an example of noncommutative space-time with potentially interesting phenomenology. However, the construction of field theories on this space is plagued with ambiguities. We propose to resolve certain ambiguities by clarifying the geometrical picture of gauge transformations on the kappa-Minkowski space-time in the twist approach. We construct the action for the noncommutative U(1) gauge fields in a geometric way, as an integral of a maximal form. The effective action with the first order corrections in the deformation parameter is obtained using the Seiberg-Witten map to relate noncommutative and commutative degrees of freedom.