# Knot and Gauge Theory

## TL;DR

This paper explores the deep connections between knot invariants like the Jones polynomial and Khovanov homology with gauge theory, revealing new insights into their mathematical and physical interpretations.

## Contribution

It establishes a link between knot invariants and gauge theory solutions, and uncovers phase transitions in topological super Yang-Mills theory.

## Key findings

- Jones polynomial computed via gauge theory solutions
- Euler characteristic of Khovanov homology related to partition functions
- Discovery of Lee-Yang type phase transition in twisted super Yang-Mills theory

## Abstract

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.