拓扑算子、不可逆对称和分解

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
Eric Sharpe
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引用次数: 0

摘要

在本文中,我们以有离散扭转和无离散扭转的二维轨道为重点,讨论了二维量子场论的单形式对称性和分解背景下的非不可逆拓扑算子。作为分析的一部分,我们研究了二维理论中表现出分解的零维算子环。从交换代数的角度来看,这些环自然与有限个点相关联,分解中的每个宇宙都有一个点。每个宇宙都与一个表示规范地相关联,该表示定义了零维算子环中的一个投影器、一个幂级数。我们讨论了体威尔逊线如何充当连接宇宙的缺陷,以及二维理论边界上的威尔逊线如何分解和计算投影器的作用。我们讨论了环的单形式对称性和相关性质。我们还给出了投影算子的一般公式,这些公式以前是根据具体情况计算的。最后,我们从表征的角度提出了非可逆高形式对称性的特征。在该表征中,分解中出现的非同构宇宙与不可反转的单形式对称性相关联。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Topological operators, noninvertible symmetries and decomposition
In this paper we discuss noninvertible topological operators in the context of one-form symmetries and decomposition of twodimensional quantum field theories, focusing on two-dimensional orbifolds with and without discrete torsion. As one component of our analysis, we study the ring of dimension-zero operators in two-dimensional theories exhibiting decomposition. From a commutative algebra perspective, the rings are naturally associated to a finite number of points, one point for each universe in the decomposition. Each universe is canonically associated to a representation, which defines a projector, an idempotent in the ring of dimension-zero operators. We discuss how bulk Wilson lines act as defects bridging universes, and how Wilson lines on boundaries of two-dimensional theories decompose, and compute actions of projectors. We discuss one-form symmetries of the rings, and related properties. We also give general formulas for projection operators, which previously were computed on a case-by-case basis. Finally, we propose a characterization of noninvertible higher-form symmetries in this context in terms of representations. In that characterization, non-isomorphic universes appearing in decomposition are associated with noninvertible one-form symmetries.
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来源期刊
Advances in Theoretical and Mathematical Physics
Advances in Theoretical and Mathematical Physics 物理-物理:粒子与场物理
CiteScore
2.20
自引率
6.70%
发文量
0
审稿时长
>12 weeks
期刊介绍: Advances in Theoretical and Mathematical Physics is a bimonthly publication of the International Press, publishing papers on all areas in which theoretical physics and mathematics interact with each other.
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