d维多环积分的一元性

IF 5.5 1区物理与天体物理 Q1 Physics and Astronomy

Journal of High Energy Physics Pub Date : 2025-10-01 DOI:10.1007/JHEP10(2025)009

Roman N. Lee, Andrei A. Pomeransky

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引用次数: 0

摘要

考虑多环积分的微分系统的单群。我们描述了一种简单的启发式方法来获得作为时空维数d的函数的单矩阵。我们观察到在一个特殊的基中，这些矩阵的元素是z = exp（iπd）的整数系数的Laurent多项式，即单群是GL（n, 0 [z, 1/z]）的一子群。从扭曲黎曼双线性关系出发，导出了d维和d维单矩阵的双线性关系，并检验了所得到的单矩阵是否满足这些双线性关系。

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Monodromy of multiloop integrals in d dimensions

We consider the monodromy group of the differential systems for multiloop integrals. We describe a simple heuristic method to obtain the monodromy matrices as functions of space-time dimension d. We observe that in a special basis the elements of these matrices are Laurent polynomials in z = exp(iπd) with integer coefficients, i.e., the monodromy group is a subgroup of GL(n, ℤ[z, 1/z]). We derive bilinear relations for monodromies in d and –d dimensions which follow from the twisted Riemann bilinear relations and check that the found monodromy matrices satisfy them.

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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).