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arXiv · 2606.28888

How to Untwist Twisted Gauge Fields

Serge Lazzarini·Thierry Masson·Louis Usala
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Abstract

This paper provides an isomorphism between the space of twisted gauge fields on a principal bundle $\mathcal{P}$ and the space of standard gauge fields on a different principal bundle $\mathcal{Q}$ associated to $\mathcal{P}$. This isomorphism extends to local fields on the base manifold, which enables the use of local twisted fields in standard gauge theories (e.g. Yang-Mills-like theories). This allows one to deal with two symmetry groups, coming from $\mathcal{P}$ and $\mathcal{Q}$, respectively. The construction makes use of a larger principal bundle $\mathcal{S}$ which has $\mathcal{P}$ and $\mathcal{Q}$ as quotient bundles. The gauge structure on $\mathcal{S}$ encodes both standard and twisted gauge structures on $\mathcal{P}$. In addition, the isomorphism classes of bundles $\mathcal{S}$ are in 1:1 correspondence with the equivalence classes of cocycles (up to a coboundary). This paper also provides a new interpretation of (full) dressing fields as dynamic (or active) sections of a principal bundle.

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Serge Lazzarini, Thierry Masson, Louis Usala. 2026-06-27. How to Untwist Twisted Gauge Fields. https://arxiv.org/abs/2606.28888

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