A twisted look on kappa-Minkowski: U(1) gauge theory

TL;DR

This paper develops a geometric approach to construct a U(1) gauge theory on kappa-Minkowski space-time using twist methods, addressing ambiguities and exploring symmetry properties, with first-order deformation corrections.

Contribution

It introduces a geometric construction of noncommutative U(1) gauge theory on kappa-Minkowski space using twists, and analyzes the symmetry and first-order corrections.

Findings

Constructed a gauge theory with a geometric action as an integral of a maximal form.

Used the Seiberg-Witten map to relate noncommutative and commutative fields.

Identified the twisted igl(1,3) symmetry replacing kappa-Poincaré symmetry.

Abstract

Kappa-Minkowski space-time is an example of noncommutative space-time with potentially interesting phenomenological consequences. However, the construction of field theories on this space, although operationally well-defined, is plagued with ambiguities. A part of ambiguities can be resolved by clarifying the geometrical picture of gauge transformations on the kappa-Minkowski space-time. To this end we use the twist approach to construct the noncommutative U(1) gauge theory coupled to fermions. However, in this approach we cannot maintain the kappa-Poincar\'e symmetry; the corresponding symmetry of the twisted kappa-Minkowski space is the twisted igl(1,3) symmetry. We construct an action for the gauge and matter fields in a geometric way, as an integral of a maximal form. We use the Seiberg-Witten map to relate noncommutative and commutative degrees of freedom and expand the action to obtain the first order corrections in the deformation parameter.