\({\hat{Z}}\)-Invariant for SO(3) and OSp(1|2) Groups

IF 1.4 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Annales Henri Poincaré Pub Date : 2023-06-06 DOI:10.1007/s00023-023-01332-y

Sachin Chauhan, Pichai Ramadevi

引用次数: 1

Abstract

Three-manifold invariants \({\hat{Z}}\) (“Z-hat”), also known as homological blocks, are q-series with integer coefficients. Explicit q-series form for \({\hat{Z}}\) is known for SU(2) group, supergroup SU(2|1) and orthosymplectic supergroup OSp(2|2). We focus on \({\hat{Z}}\) for SO(3) group and orthosymplectic supergroup OSp(1|2) in this paper. Particularly, the change of variable relating SU(2) link invariants to the SO(3) and OSp(1|2) link invariants plays a crucial role in explicitly writing the q-series.

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\({\hat{Z}}\)- SO(3)和OSp(1|2)群的不变性

三流形不变量\({\hat{Z}}\)(“Z-hat”)，也称为同调块，是具有整数系数的q级数。已知\({\hat{Z}}\)的显式q级数形式为SU(2)群、超群SU(2|1)和正辛超群OSp(2|2)。本文主要讨论了SO(3)群和正辛超群OSp(1|2)的\({\hat{Z}}\)。特别是，SU(2)链接不变量与SO(3)和OSp(1|2)链接不变量之间的变量变化在显式写出q级数时起着至关重要的作用。

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

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.