发表机构
CEU San Pablo University（塞乌圣巴勃罗大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究构造了弱李3-群$T_2 \mathbb B^{F_1}_n$，证明其与另一李3-群的同伦等价，为建立环面纤维化上2-gerbes的高阶T-对偶奠定基础，相关于超引力与M理论。
AI 中文摘要
我们从ℝⁿ/ℤⁿ上的gerbes的2-范畴以及其沿平移的拉回作用的ℝⁿ/ℤⁿ作用出发，构造了弱李3-群$T_2 \mathbb B^{F_1}_n$。我们还构造了$T_2 \mathbb B^{F_1}_n$与另一李3-群$T_2 \mathbb D^{F_1}_n$之间的同伦等价，该等价可约化到Nikolaus与Waldorf引入的李2-群的同伦等价，用于建模半几何T-对偶。这是建立与超引力和M理论相关的、环面纤维化上2-gerbes的高阶T-对偶的第一步。
英文摘要
We construct a weak Lie 3-group $T_2 \mathbb B^{F_1}_n$ from the 2-category of gerbes over $\mathbb R^n / \mathbb Z^n$ and the $\mathbb R^n/ \mathbb Z^n$-action on it by pullback along translations. We also construct a homotopy equivalence between $T_2 \mathbb B^{F_1}_n$ and a different Lie 3-group $T_2 \mathbb D^{F_1}_n$, 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.
Comments40 pages
