# Critical exponents and abelian dominance in $SU(2)$ QCD

## TL;DR

This paper investigates the critical behavior of abelian and non-abelian Polyakov loops in finite temperature $SU(2)$ QCD, demonstrating abelian dominance and matching critical exponents through finite-size scaling analysis.

## Contribution

It provides quantitative evidence of abelian dominance and shows that abelian Polyakov loops share the same critical point and exponents as non-abelian loops in $SU(2)$ QCD.

## Key findings

- Abelian Polyakov loop critical point matches non-abelian within errors.
- Critical exponents agree between abelian and non-abelian loops.
- Abelian dominance is quantitatively confirmed.

## 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. We evaluate the critical point and the critical exponents from each Polyakov loop in the maximally abelian gauge using the finite-size scaling analysis. Abelian dominance in this case is proved quantitatively. The critical point of each abelian Polyakov loop is equal to that of the non-abelian Polyakov loop within the statistical errors. Also, the critical exponents are in good agreement with those from non-abelian Polyakov loops.