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PreprintCC BY 4.0arXiv

Principal bundles in supersymmetry

  • Akira Masuoka
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Abstract

We discuss rather basic problems on super principal bundles for C∞-supermanifolds (over ℝ) and analytic supermanifolds over a complete field of arbitrary characteristic. Sharper answers are obtained for C∞-supermanifolds and for homogeneous supermanifolds. Among others, it is proved for C∞-supermanifolds that given a C∞-supermanifold B and a super Lie group G, there is a natural one-to-one correspondence (up to isomorphism) between the G-super principal bundles over B and the Grd-principal bundles over Brd, where Grd (resp., Brd) denotes the ordinary Lie group (resp., manifold) associated with G (resp., B). To prove this, we show a generalized, equivariant version of the renowned Batchelor Theorem.

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Cite

BibTeXRIS
BibTeX
@misc{masuoka2026principal,
  title = {{Principal bundles in supersymmetry}},
  author = {Akira Masuoka},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25811},
  eprint = {2610.25811},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25811},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Principal bundles in supersymmetry
AU  - Akira Masuoka
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.25811
UR  - https://arxiv.org/abs/2610.25811
AB  - We discuss rather basic problems on super principal bundles for C^∞-supermanifolds (over ℝ) and analytic supermanifolds over a complete field of arbitrary characteristic. Sharper answers are obtained for C^∞-supermanifolds and for homogeneous supermanifolds. Among others, it is proved for C^∞-supermanifolds that given a C^∞-supermanifold B and a super Lie group G, there is a natural one-to-one correspondence (up to isomorphism) between the G-super principal bundles over B and the G_rd-principal bundles over B_rd, where G_rd (resp., B_rd) denotes the ordinary Lie group (resp., manifold) associated with G (resp., B). To prove this, we show a generalized, equivariant version of the renowned Batchelor Theorem.
ER  -