Generalized Pentagon Equations

IF 1.4 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL
Anton Alekseev, Florian Naef, Muze Ren
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引用次数: 0

Abstract

Drinfeld defined the Knizhnik–Zamolodchikov (KZ) associator \(\Phi _{\textrm{KZ}}\) by considering the regularized holonomy of the KZ connection along the droit chemin [0, 1]. The KZ associator is a group-like element of the free associative algebra with two generators, and it satisfies the pentagon equation. In this paper, we consider paths on \({\mathbb {C}}\backslash \{ z_1, \dots , z_n\}\) which start and end at tangential base points. These paths are not necessarily straight, and they may have a finite number of transversal self-intersections. We show that the regularized holonomy H of the KZ connection associated with such a path satisfies a generalization of Drinfeld’s pentagon equation. In this equation, we encounter H, \(\Phi _{\textrm{KZ}}\), and new factors associated with self-intersections, tangential base points, and the rotation number of the path.

广义五边形方程
Drinfeld通过考虑KZ连接沿右链的正则完整性,定义了kizhnik - zamolodchikov (KZ)关联子\(\Phi _{\textrm{KZ}}\)[0,1]。KZ关联子是具有两个生成器的自由关联代数的类群元素,它满足五边形方程。在本文中,我们考虑\({\mathbb {C}}\backslash \{ z_1, \dots , z_n\}\)上的路径开始和结束于切线基点。这些路径不一定是直的,它们可能有有限数量的横向自交点。我们证明了与这种路径相关的KZ连接的正则完整H满足德林菲尔德五边形方程的推广。在这个方程中,我们遇到H、\(\Phi _{\textrm{KZ}}\)和与自交、切向基点和路径旋转数相关的新因子。
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来源期刊
Annales Henri Poincaré
Annales Henri Poincaré 物理-物理:粒子与场物理
CiteScore
3.00
自引率
6.70%
发文量
108
审稿时长
6-12 weeks
期刊介绍: The two journals Annales de l''Institut Henri Poincaré, physique théorique and Helvetica Physical Acta merged into a single new journal under the name Annales Henri Poincaré - A Journal of Theoretical and Mathematical Physics edited jointly by the Institut Henri Poincaré and by the Swiss Physical Society. The goal of the journal is to serve the international scientific community in theoretical and mathematical physics by collecting and publishing original research papers meeting the highest professional standards in the field. The emphasis will be on analytical theoretical and mathematical physics in a broad sense.
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