The four-components link invariant in the framework of topological field theories

IF 3 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Annals of Physics Pub Date : 2024-09-12 DOI:10.1016/j.aop.2024.169804
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Abstract

In this work, we undertake a perturbative analysis of the topological non-Abelian Chern–Simons-Wong model with the aim to explicitly construct the second-order on-shell action. The resulting action is a topological quantity depending solely on closed curves, so it correspond to an analytical expression of a link invariant. Additionally, we construct an Abelian model that reproduces the same second-order on-shell action as its non-Abelian Chern–Simons-Wong counterpart so it functions as an intermediate model, featuring Abelian fields generated by currents supported on closed paths. By geometrically analyzing each term, we demonstrate that this topological invariant effectively detects the knotting of a four-component link.

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拓扑场论框架中的四组件链接不变性
在这项工作中,我们对拓扑非阿贝尔切尔恩-西蒙斯-王模型进行了扰动分析,目的是明确地构建二阶壳上作用。由此得到的作用是一个拓扑量,只取决于封闭曲线,因此它对应于一个链路不变量的分析表达式。此外,我们还构建了一个阿贝尔模型,该模型重现了与非阿贝尔的切尔-西蒙斯-王模型相同的二阶壳上作用,因此它可以作为一个中间模型,具有由闭合路径上支持的电流产生的阿贝尔场。通过对每个项的几何分析,我们证明了这种拓扑不变量能有效地检测四分量链路的打结。
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来源期刊
Annals of Physics
Annals of Physics 物理-物理:综合
CiteScore
5.30
自引率
3.30%
发文量
211
审稿时长
47 days
期刊介绍: Annals of Physics presents original work in all areas of basic theoretic physics research. Ideas are developed and fully explored, and thorough treatment is given to first principles and ultimate applications. Annals of Physics emphasizes clarity and intelligibility in the articles it publishes, thus making them as accessible as possible. Readers familiar with recent developments in the field are provided with sufficient detail and background to follow the arguments and understand their significance. The Editors of the journal cover all fields of theoretical physics. Articles published in the journal are typically longer than 20 pages.
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