# Topological Field Theory and Phase Transition

## TL;DR

This paper explores the relationship between topological field theories, Jones polynomials, and phase transitions, revealing Lee-Yang type zeros and phase transitions in these mathematical and physical frameworks.

## Contribution

It demonstrates that zeros of the Jones polynomial correspond to Lee-Yang type phase transitions within topological twisted super Yang-Mills theory.

## Key findings

- Jones polynomial zeros are Lee-Yang type.
- Lee-Yang phase transition analyzed in Jones polynomial of torus knots.
- Partition function expansion relates to Wilson loop expectation values.

## Abstract

The partition function of the topological twisted super Yang-Mills field theory on the boundary can be expanded as Jones polynomial, which can be computed as expectation values of Wilson loop operators. We show that the zero of the Jones polynomial is Lee-Yang type. Moreover, Lee-Yang phase transition is also discussed in the Jones polynomial of torus knot and the topological twisted super Yang-Mills field theory.