arXiv 2406.026762024-06hep-th

规范非可逆对称性中的离散挠率

Discrete torsion in gauging non-invertible symmetries

Alonso Perez-Lona

备注：: Clarified multi-loop factorization section; included reference to more examples

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AI总结：

本文研究二维QFT中非可逆对称性的离散挠率推广，提出两种互补推广，并阐明其中一种编码B场作用，推广了普通orbifold结果。

摘要：

在本文中，我们讨论了二维量子场论中非可逆对称性的离散挠率的推广。本文的一个要点是解释存在两种互补的推广。当特化到普通有限群G时，这两种推广都由H^2(G,U(1))计数。然而，对于更一般的融合范畴，计数是不同的。此外，只有一种推广将离散挠率作为B场上规范作用选择的差异这一图景加以推广。详细解释这一点，即离散挠率到非可逆情形的两种推广之一如何编码对B场的作用，是本文的另一个要点。特别是，这推广了普通orbifold中的旧结果，即离散挠率是B场上群作用的一种选择。我们还解释了离散挠率的同一种推广如何在对可规范代数和纤维函子产生物理上合理的扭转。

英文摘要：

In this paper we discuss generalizations of discrete torsion to noninvertible symmetries in 2d QFTs. One point of this paper is to explain that there are two complementary generalizations. Both generalizations are counted by $H^2(G,U(1))$ when one specializes to ordinary finite groups $G$. However, the counting is different for more general fusion categories. Furthermore, only one generalizes the picture of discrete torsion as differences in choices of gauge actions on B fields. Explaining this in detail, how one of the generalizations of discrete torsion to noninvertible cases encodes actions on B fields, is the other point of this paper. In particular, this generalizes old results in ordinary orbifolds that discrete torsion is a choice of group action on the B field. We also explain how this same generalization of discrete torsion gives rise to physically-sensible twists on gaugeable algebras and fiber functors.

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