How to Untwist Twisted Gauge Fields

Abstract

This paper provides an isomorphism between the space of twisted gauge fields on a principal bundle 𝒫(M,H) and the space of standard gauge fields on a different principal bundle 𝒬(M,G) associated to 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 𝒫 and 𝒬, respectively. The construction makes use of a larger principal bundle 𝒮 which has 𝒫 and 𝒬 as quotient bundles. 𝒮 is a Hilsum-Skandalis bibundle between the action groupoids Hltimes𝒫 and Gltimes𝒬. The gauge structure on 𝒮 encodes both standard and twisted gauge structures on 𝒫. In addition, the isomorphism classes of bundles 𝒮 up to an isomorphism covering the identity map on 𝒫 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.

Versions

10.1016/j.geomphys.2026.106028Published version10.1016/j.geomphys.2026.106028

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BibTeX RIS

BibTeX

@misc{lazzarini2026untwist,
  title = {{How to Untwist Twisted Gauge Fields}},
  author = {Serge Lazzarini and Thierry Masson and Louis Usala},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.28888},
  eprint = {2606.28888},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.28888},
}

RIS

TY  - UNPB
TI  - How to Untwist Twisted Gauge Fields
AU  - Serge Lazzarini
AU  - Thierry Masson
AU  - Louis Usala
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2606.28888
UR  - https://arxiv.org/abs/2606.28888
AB  - This paper provides an isomorphism between the space of twisted gauge fields on a principal bundle 𝒫(M,H) and the space of standard gauge fields on a different principal bundle 𝒬(M,G) associated to 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 𝒫 and 𝒬, respectively. The construction makes use of a larger principal bundle 𝒮 which has 𝒫 and 𝒬 as quotient bundles. 𝒮 is a Hilsum-Skandalis bibundle between the action groupoids Hltimes𝒫 and Gltimes𝒬. The gauge structure on 𝒮 encodes both standard and twisted gauge structures on 𝒫. In addition, the isomorphism classes of bundles 𝒮 up to an isomorphism covering the identity map on 𝒫 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.
ER  -

Abstract

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