On refined Vogel's universality

IF 4.3 2区物理与天体物理 Q1 ASTRONOMY & ASTROPHYSICS

Physics Letters B Pub Date : 2025-05-20 DOI:10.1016/j.physletb.2025.139596

Liudmila Bishler , Andrei Mironov

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引用次数: 0

Abstract

In accordance with P. Vogel, a set of algebra structures in Chern-Simons theory can be made universal, independent of a particular family of simple Lie algebras. In particular, this means that various quantities in the adjoint representations of these simple Lie algebras such as dimensions and quantum dimensions, Racah coefficients, etc. are simple rational functions of two parameters on Vogel's plane, giving three lines associated with sl,

s o / s p

and exceptional algebras correspondingly. By analyzing the partition function of refined of Chern-Simons theory, it was suggested earlier that the refinement may preserve the universality for simply laced algebras. Here we support this conjecture by analyzing the Macdonald dimensions, i.e. values of Macdonald polynomials at

q^{ρ}

, where ρ is the Weyl vector: there is a universality formula that describes these dimensions for the simply laced algebras as a function on the Vogel's plane.

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论改进的傅高义的普遍性

根据P. Vogel， chen - simons理论中的一组代数结构可以是普适的，独立于某一类简单李代数。特别地，这意味着这些简单李代数的伴随表示中的各种量，如维数和量子维数、Racah系数等，是Vogel平面上两个参数的简单有理数函数，从而给出与sl、so/sp和例外代数相对应的三条直线。通过分析改进后的chen - simons理论的配分函数，提出了改进后的chen - simons理论可以保持简系代数的普适性。在这里，我们通过分析麦克唐纳维来支持这一猜想，即麦克唐纳多项式在qρ处的值，其中ρ是Weyl向量：有一个普适公式将简单代数的这些维描述为Vogel平面上的函数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Physics Letters B 物理-物理：综合

CiteScore

9.10

自引率

6.80%

发文量

647

审稿时长

3 months

期刊介绍： Physics Letters B ensures the rapid publication of important new results in particle physics, nuclear physics and cosmology. Specialized editors are responsible for contributions in experimental nuclear physics, theoretical nuclear physics, experimental high-energy physics, theoretical high-energy physics, and astrophysics.