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Differential T2-Duality and Spans of Principal 3-Bundles with Connections

  • Gianni Gagliardo
  • Christian Saemann
  • Roberto Tellez-Dominguez
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Abstract

We present a generalization of T-duality, called T2-duality, that captures certain aspects of U-duality in M-theory. In particular, it features backgrounds that contain a 2-gerbe over a principal torus bundle, structures familiar from eleven-dimensional supergravity backgrounds. In special cases, it also incorporates S-duality in a precise sense. Our main result is a theorem characterizing T2-dual pairs through spans of categorified principal bundles with connections, giving explicit rules for constructing a T2-dual for a given background. A number of explicit examples illustrate how the various characteristic classes are mapped between the left and right backgrounds. For two-dimensional torus fibers, we also relate our construction to the combination of dimensional reduction and T-duality that links eleven-dimensional supergravity to type IIB supergravity. Finally, we discuss how T2-duality arises from a Buscher-like span of 3d sigma models.

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Cite

BibTeXRIS
BibTeX
@misc{gagliardo2026differential,
  title = {{Differential $T_2$-Duality and Spans of Principal 3-Bundles with Connections}},
  author = {Gianni Gagliardo and Christian Saemann and Roberto Tellez-Dominguez},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.12383},
  eprint = {2610.12383},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.12383},
}
RIS
TY  - UNPB
TI  - Differential T_2-Duality and Spans of Principal 3-Bundles with Connections
AU  - Gianni Gagliardo
AU  - Christian Saemann
AU  - Roberto Tellez-Dominguez
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.12383
UR  - https://arxiv.org/abs/2610.12383
AB  - We present a generalization of T-duality, called T_2-duality, that captures certain aspects of U-duality in M-theory. In particular, it features backgrounds that contain a 2-gerbe over a principal torus bundle, structures familiar from eleven-dimensional supergravity backgrounds. In special cases, it also incorporates S-duality in a precise sense. Our main result is a theorem characterizing T_2-dual pairs through spans of categorified principal bundles with connections, giving explicit rules for constructing a T_2-dual for a given background. A number of explicit examples illustrate how the various characteristic classes are mapped between the left and right backgrounds. For two-dimensional torus fibers, we also relate our construction to the combination of dimensional reduction and T-duality that links eleven-dimensional supergravity to type IIB supergravity. Finally, we discuss how T_2-duality arises from a Buscher-like span of 3d sigma models.
ER  -