# Critical exponents in abelian projected $SU(2)$ QCD

## TL;DR

This paper investigates the critical behavior of abelian Polyakov loops in finite temperature $SU(2)$ QCD, finding critical points and exponents consistent with non-abelian results, using finite-size scaling in the maximally abelian gauge.

## Contribution

It provides the first detailed analysis of abelian Polyakov loop critical properties in abelian projected $SU(2)$ QCD, confirming their agreement with non-abelian counterparts.

## Key findings

- Critical points match non-abelian results.
- Critical exponents are consistent with non-abelian QCD.
- Finite-size scaling analysis validates abelian projection approach.

## Abstract

The critical properties of the abelian Polyakov loop and the Polyakov loop in terms of Dirac string are studied in finite temperature abelian projected $SU(2)$ QCD. The critical point and the critical exponents are determined from each Polyakov loop in the maximally abelian gauge using the finite-size scaling analyses. Those critical points and exponents are in good agreement with those from non-abelian Polyakov loops.