arXiv 2209.033432022-09hep-thmath.AT

广义对称算符背后的膜

The Branes Behind Generalized Symmetry Operators

Jonathan J. Heckman, Max Hübner, Ethan Torres, Hao Y. Zhang

备注：: v3: 21 pages + references, 1 figure; clarifications added, reference added
DOI：: 10.1002/prop.202200180

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AI总结：

本文提出通过弦构造中膜在非紧几何边界上的磁对偶膜来系统读出广义对称算符的世界体理论和融合规则，并以6D超共形场论的F理论实现为例，揭示了3维缺陷所检测的非可逆融合规则。

摘要：

现代方法处理 d 维量子场论（QFT）中的 m-形式全局对称性时，需要指定维度为 d-m-1 的拓扑广义对称算符，这些算符与 m 维缺陷算符具有非平凡的链接关系。在通过非紧几何 X 上的弦构造所实现的 QFT 中，这些缺陷来源于包裹在非紧循环上的膜，这些循环从局域源或奇点延伸至边界 ∂X。与这些缺陷相链接的广义对称算符则来源于包裹在 ∂X 中循环上的磁对偶膜。这提供了一种系统性的方法，可以读出此类拓扑算符的各种性质，包括其世界体拓扑场论以及由此产生的融合规则。我们在 6D 超共形场论的背景下阐释这些一般特征，利用这些理论的 F 理论实现来读出广义对称算符上的世界体理论。带电于合适 3-形式对称性的 3 维缺陷可检测到这些算符的非可逆融合规则。我们还概述了类似考量如何适用于相关系统。

英文摘要：

The modern approach to $m$-form global symmetries in a $d$-dimensional quantum field theory (QFT) entails specifying dimension $d-m-1$ topological generalized symmetry operators which non-trivially link with $m$-dimensional defect operators. In QFTs engineered via string constructions on a non-compact geometry $X$, these defects descend from branes wrapped on non-compact cycles which extend from a localized source / singularity to the boundary $\partial X$. The generalized symmetry operators which link with these defects arise from magnetic dual branes wrapped on cycles in $\partial X$. This provides a systematic way to read off various properties of such topological operators, including their worldvolume topological field theories, and the resulting fusion rules. We illustrate these general features in the context of 6D superconformal field theories, where we use the F-theory realization of these theories to read off the worldvolume theory on the generalized symmetry operators. Defects of dimension 3 which are charged under a suitable 3-form symmetry detect a non-invertible fusion rule for these operators. We also sketch how similar considerations hold for related systems.

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