Gauge theory models on $\kappa$-Minkowski space: Results and prospects

TL;DR

This paper reviews gauge theories on $ kappa$-Minkowski space, highlighting the mathematical structures, dimensional constraints, and phenomenological implications of noncommutative gauge models, including one-loop quantum effects.

Contribution

It presents a comprehensive review of gauge theories on $ kappa$-Minkowski space, emphasizing the star product, differential calculus, and BRST structure, with new insights into dimensional restrictions and quantum effects.

Findings

Gauge invariant actions exist only in 5 dimensions.

A star product derived from Weyl quantization facilitates gauge theory formulation.

One-loop tadpole contributions indicate quantum corrections in the model.

Abstract

Recent results obtained in $\kappa$-Poincar\'e invariant gauge theories on $\kappa$-Minkowski space are reviewed and commented. A Weyl quantization procedure can be applied to convolution algebras to derive a convenient star product. For such a star product, gauge invariant polynomial action functional depending on the curvature exists only in 5 dimensions. The corresponding noncommutative differential calculus and the related connection are twisted together with the BRST structure linked to the gauge invariance. Phenomenological consequences stemming from the existence of one extra dimension are commented. Some consequences of the appearance of a non-vanishing one-loop tadpole upon BRST gauge-fixing are discussed.