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arXiv · 2508.19346

On a non-geometric approach to noncommutative gauge theories

Guilherme Barrocas·Aleksandr Pinzul
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Abstract

In this work, we generalize the non-geometrical construction of gauge theories, due to S. Deser, to a noncommutative setting. We show that in a free theory, along with the usual local N\"{o}ther current, there is another conserved current, which is non-local. Using the latter as a source for self-interaction, after a well-defined consistency procedure, we arrive at noncommutative gauge theories. In the non-abelian case, the standard restriction, namely that the theory should be $U(N)$ in the fundamental representation, emerges as a consequence of the requirement that the non-local current be Lie algebra valued.

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Guilherme Barrocas, Aleksandr Pinzul. 2025-08-26. On a non-geometric approach to noncommutative gauge theories. https://arxiv.org/abs/2508.19346

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