d > 2 自由共形场论中的模块性

IF 5.4 1区物理与天体物理 Q1 Physics and Astronomy

Journal of High Energy Physics Pub Date : 2024-11-06 DOI:10.1007/JHEP11(2024)023

Yang Lei, Sam van Leuven

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引用次数: 0

摘要

我们推导出了 S2D-1 × S1 上自由共形耦合标量的分区函数的新封闭式表达式，这些表达式重述了精确的高温展开。这种推导依赖于分割函数与多重椭圆伽马函数的辨识，这些函数在化学势和温度中是分析持续的。这些函数满足有趣的模态特性，我们利用这些特性得出我们的表达式。我们描述了超共形场论背景下多重椭圆伽马函数模块性质的几何解释。在此基础上，我们提出了偶数维自由标量 CFT 背景下模块性质的几何解释，并对奇数维和自由费米子的扩展进行了评论。

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Modularity in d > 2 free conformal field theory

We derive new closed form expressions for the partition functions of free conformally-coupled scalars on S^2D−1 × S¹ which resum the exact high-temperature expansion. The derivation relies on an identification of the partition functions, analytically continued in chemical potentials and temperature, with multiple elliptic Gamma functions. These functions satisfy interesting modular properties, which we use to arrive at our expressions. We describe a geometric interpretation of the modular properties of multiple elliptic Gamma functions in the context of superconformal field theory. Based on this, we suggest a geometric interpretation of the modular property in the context of the free scalar CFT in even dimensions and comment on extensions to odd dimensions and free fermions.

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来源期刊

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).