微分$T_2$-对偶与带联络的主3-丛的张景
Differential $T_2$-Duality and Spans of Principal 3-Bundles with Connections
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- Maxwell Institute for Mathematical Sciences Department of Mathematics, Heriot–Watt University（赫瑞-瓦特大学数学系）
- CEU San Pablo University（CEU圣巴勃罗大学）
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中文总结 AI 辅助
本文提出推广T-对偶的$T_2$-对偶，通过带联络的范畴化主丛张景刻画其对偶对，结合维度约化关联超引力，还讨论其源于类Buscher的3d sigma模型张景。
中文摘要 AI 辅助
我们提出了T-对偶的一种推广，称为$T_2$-对偶，它能捕捉M理论中U-对偶的某些方面。特别地，该理论包含主环丛上的2-gerbe背景，这是十一维超引力背景中的常见结构。在特殊情形下，它还以精确的方式包含S-对偶。我们的主要结果是一个定理，通过带联络的范畴化主丛的张景来刻画$T_2$-对偶对，给出了为给定背景构造$T_2$-对偶的明确规则。多个明确的例子展示了各类示性类如何在左右背景间映射。对于二维环纤维，我们还将我们的构造与维度约化和T-对偶的组合联系起来，该组合将十一维超引力与IIB型超引力关联。最后，我们讨论$T_2$-对偶如何源于类Buscher的3d sigma模型张景。
英文摘要
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.
