The Maximal Abelian Gauge in SU(N) Gauge Theories and Thermal Monopoles for N = 3

TL;DR

This paper extends the Abelian projection method to SU(N) gauge theories and investigates thermal monopoles in SU(3), revealing their properties and interactions in the deconfined phase.

Contribution

It proposes a proper extension of the Abelian projection for SU(N) and studies thermal monopoles in SU(3), highlighting their properties and interactions.

Findings

Thermal monopoles exhibit similar properties in SU(3) as in SU(2).

Magnetic components are relevant near the deconfinement temperature Tc.

Monopole correlation functions show non-trivial interactions.

Abstract

We discuss and propose a proper extension of the Abelian projection based on the Maximal Abelian Gauge to SU(N) gauge theories. Based, on that, we investigate the properties of thermal Abelian monopoles in the deconfined phase of the SU(3) pure gauge theory. Such properties are very similar to those already found for SU(2), confirming the relevance of the magnetic component close to Tc and the possible condensation of thermal monopoles as the deconfinement temperature is crossed from above. Moreover, we study the correlation functions among monopoles related to different U(1) subgroups, which show interesting features and reveal the presence of non-trivial interactions.