# Monopoles and the Chiral Phase Transition in $SU(2)$ Lattice Gauge Theory

## TL;DR

This study investigates the relationship between monopoles, abelian projection, and the chiral phase transition in SU(2) lattice gauge theory, finding that monopole-related abelian fields accurately predict the critical temperature of the transition.

## Contribution

It demonstrates that the chiral condensate derived from abelian projection vanishes at the same critical temperature as the full SU(2) theory, highlighting the role of monopoles in the phase transition.

## Key findings

- Abelian projection reproduces the critical temperature of the chiral transition.
- Monopole fields are closely linked to the chiral phase transition.
- Chiral condensate vanishes at the critical temperature in the abelian projected theory.

## Abstract

In the quenched approximation we use the abelian and monopole fields from abelian projection in SU(2) lattice gauge theory to numerically compute the value of the chiral condensate. The condensate calculated using abelian projection is observed to vanish at the same critical temperature as the full SU(2) theory predicts.