自镜像对称scft的时间反转不变tqft

IF 5.4 1区 物理与天体物理 Q1 Physics and Astronomy
Hongliang Jiang
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引用次数: 0

摘要

我们建立了三维自镜像对称\( \mathcal{N} \) = 4超共形场论(SCFTs)和由普遍质量变形引起的时间反转不变拓扑量子场论(TQFTs)之间的联系。在阿贝尔情况下,紫外(UV) SCFT的特征是电荷矩阵Q,而红外(IR) TQFT对应于能级矩阵K = QQT的阿贝尔chen - simons理论。我们推导了自镜像对称SCFTs电荷矩阵的约束条件,并证明了这些理论的库仑和希格斯分支希尔伯特级数是一致的。此外,我们还导出了任意电荷矩阵的Abelian \( \mathcal{N} \) = 4 SCFTs超共形指标的一般公式。对于带有约束电荷矩阵的SCFT,我们论证了超共形指数在与r对称相关的失度反演下表现出不变性,进一步证明了自镜像对称性。我们详细探讨了时间反转不变Abelian chen - simons理论的各种性质,并从多个角度建立了它们与SCFTs自镜像对称性的联系。特别地,我们引入了一个量,称为高斯生成函数,它是实的,因此在复共轭下对于时间反转对称tqft是不变的,与超共形指数平行,它在自镜像对称scft的r -对称度反转下是不变的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Time-reversal invariant TQFTs from self-mirror symmetric SCFTs

We establish a connection between three-dimensional self-mirror symmetric \( \mathcal{N} \) = 4 superconformal field theories (SCFTs) and time-reversal invariant topological quantum field theories (TQFTs) arising from universal mass deformations. Focusing on the Abelian case, the ultraviolet (UV) SCFT is characterized by the charge matrix Q, while the infrared (IR) TQFT corresponds to an Abelian Chern-Simons theory with level matrix K = QQT. We derive constraints on the charge matrix for self-mirror symmetric SCFTs and demonstrate that the Coulomb and Higgs branch Hilbert series of these theories coincide. Additionally, we derive a general formula for the superconformal indices of Abelian \( \mathcal{N} \) = 4 SCFTs with arbitrary charge matrices. For SCFT with the constrained charge matrix, the superconformal index is argued to exhibit invariance under the inversion of fugacity associated with R-symmetry, providing further evidence of self-mirror symmetry. We explore various properties of time-reversal invariant Abelian Chern-Simons theories in detail and establish their connections to self-mirror symmetry in SCFTs from multiple perspectives. In particular, we introduce a quantity, dubbed Gauss generating function, which is real and thus invariant under complex conjugation for time-reversal symmetric TQFTs, in parallel with the superconformal index, which is invariant under the inversion of R-symmetry fugacity for self-mirror symmetric SCFTs.

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来源期刊
Journal of High Energy Physics
Journal of High Energy Physics 物理-物理:粒子与场物理
CiteScore
10.30
自引率
46.30%
发文量
2107
审稿时长
1.5 months
期刊介绍: The aim of the Journal of High Energy Physics (JHEP) is to ensure fast and efficient online publication tools to the scientific community, while keeping that community in charge of every aspect of the peer-review and publication process in order to ensure the highest quality standards in the journal. Consequently, the Advisory and Editorial Boards, composed of distinguished, active scientists in the field, jointly establish with the Scientific Director the journal''s scientific policy and ensure the scientific quality of accepted articles. JHEP presently encompasses the following areas of theoretical and experimental physics: Collider Physics Underground and Large Array Physics Quantum Field Theory Gauge Field Theories Symmetries String and Brane Theory General Relativity and Gravitation Supersymmetry Mathematical Methods of Physics Mostly Solvable Models Astroparticles Statistical Field Theories Mostly Weak Interactions Mostly Strong Interactions Quantum Field Theory (phenomenology) Strings and Branes Phenomenological Aspects of Supersymmetry Mostly Strong Interactions (phenomenology).
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