A gauge invariant study of the monopole condensation in non Abelian lattice gauge theories

TL;DR

This paper introduces a gauge-invariant disorder parameter to study Abelian monopole condensation in finite temperature SU(2) and SU(3) lattice gauge theories, revealing monopole condensation in the confined phase and its disappearance at deconfinement.

Contribution

It presents a novel gauge-invariant method to analyze monopole condensation in non-Abelian lattice gauge theories, including a comparison of different Abelian monopole definitions.

Findings

Monopole condensation occurs in the confined phase.

The disorder parameter tends to zero at the deconfinement transition.

Different Abelian monopoles are compared in SU(3) gauge theory.

Abstract

We investigate the Abelian monopole condensation in finite temperature SU(2) and SU(3) pure lattice gauge theories. To this end we introduce a gauge invariant disorder parameter built up in terms of the lattice Schr\"odinger functional. Our numerical results show that the disorder parameter is different from zero and Abelian monopole condense in the confined phase. On the other hand our numerical data suggest that the disorder parameter tends to zero, in the thermodynamic limit, when the gauge coupling constant approaches the critical deconfinement value. In the case of SU(3) we also compare the different kinds of Abelian monopoles which can be defined according to the choice of the Abelian subgroups.