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arXiv · 2510.19112

Noncommutative Gauge Theories: Yang-Mills extensions and beyond - An overview

Jean-Christophe Wallet
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Abstract

The status of several representative gauge theories on various quantum space-times, mainly focusing on Yang-Mills type extensions together with a few matrix model formulations is overviewed. The common building blocks are derivation based differential calculus possibly twisted and noncommutative analog of the Koszul connection. The star-products related to the quantum space-times are obtained from a combination of harmonic analysis of group algebras combined with Weyl quantization. The remaining problems inherent to gauge theories on Moyal spaces in their two different formulations are outlined. A family of gauge invariant matrix models on $\mathbb{R}^3_\lambda$, a deformation of $\mathbb{R}^3$ is presented among which a solvable model. The characterization of 11 new quantum Minkowski space-times through their $*$-algebras is given. A gauge theory of Yang-Mills type is constructed on one recently explored of these space-times and compared to its counterpart built on the popular $\kappa$-Minkowski.

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Jean-Christophe Wallet. 2025-10-21. Noncommutative Gauge Theories: Yang-Mills extensions and beyond - An overview. https://arxiv.org/abs/2510.19112

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