Knot and Gauge Theory

It has been argued based on electric-magnetic duality that the Jones polynomial of a knot in three dimensions can be computed by counting the solutions of certain gauge theory equations in four-dimension. And the Euler characteristic of Khovanov homology is the Jones polynomial which corresponds to...

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Bibliographic Details
Published in:arXiv.org 2019-04
Main Authors: Zhou, Jing, Jialun Ping
Format: Article
Language:English
Subjects:
Gauge theory
Homology
Partitions (mathematics)
Phase transitions
Polynomials
Yang-Mills theory
Online Access:Get full text
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Summary:It has been argued based on electric-magnetic duality that the Jones polynomial of a knot in three dimensions can be computed by counting the solutions of certain gauge theory equations in four-dimension. And the Euler characteristic of Khovanov homology is the Jones polynomial which corresponds to the partition function of twisted \(N=4\) super Yang-Mills theory. Moreover, Lee-Yang type phase transition is found in the topological twisted super Yang-Mills theory.
ISSN:2331-8422