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Weak Lie 3-groups, 2-gerbes over torus fibrations of type F1, and T-Duality
Abstract
We construct a weak Lie 3-group T2 πΉF1n from the 2-category of gerbes over βn / β€n and the βn/ β€n-action on it by pullback along translations. We also construct a homotopy equivalence between T2 πΉF1n and a different Lie 3-group T2 π»F1n, which admits a dimensional reduction to the homotopy equivalence of Lie 2-groups introduced by Nikolaus and Waldorf to model half-geometric T-duality. This is a first step towards establishing a higher form of T-duality for 2-gerbes over torus fibrations, relevant to supergravity and M-theory.
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BibTeX
@misc{tellezdominguez2026weak,
title = {{Weak Lie 3-groups, 2-gerbes over torus fibrations of type F1, and T-Duality}},
author = {Roberto Tellez-Dominguez},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04934},
eprint = {2609.04934},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04934},
}
RIS
TY - UNPB
TI - Weak Lie 3-groups, 2-gerbes over torus fibrations of type F1, and T-Duality
AU - Roberto Tellez-Dominguez
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.04934
UR - https://arxiv.org/abs/2609.04934
AB - We construct a weak Lie 3-group T_2 πΉ^F_1_n from the 2-category of gerbes over β^n / β€^n and the β^n/ β€^n-action on it by pullback along translations. We also construct a homotopy equivalence between T_2 πΉ^F_1_n and a different Lie 3-group T_2 π»^F_1_n, which admits a dimensional reduction to the homotopy equivalence of Lie 2-groups introduced by Nikolaus and Waldorf to model half-geometric T-duality. This is a first step towards establishing a higher form of T-duality for 2-gerbes over torus fibrations, relevant to supergravity and M-theory.
ER -