Are there monopoles in the quark-gluon plasma?

TL;DR

This paper explores the potential existence of monopole-like objects in the quark-gluon plasma by connecting instanton-dyons and monopoles through semiclassical partition functions, bridging gaps in understanding their phenomenological roles.

Contribution

It demonstrates how instanton-based partition functions in pure gauge theories can be transformed into monopole partition functions, suggesting monopoles' relevance in QCD-like theories.

Findings

Instanton-dyons relate to monopoles via Poisson transformation.

Partition functions of instantons and monopoles are connected.

Monopoles may play a role in the quark-gluon plasma phenomenology.

Abstract

Monopole-like objects have been identified in multiple lattice studies, and there is now a significant amount of literature on their importance in phenomenology. Some analytic indications of their role, however, are still missing. The 't Hooft-Polyakov monopoles, originally derived in the Georgi-Glashow model, are an important dynamical ingredient in theories with extended supersymmetry ${\cal N} = 2,\,4$, and help explain the issues related with electric-magnetic duality. There is no such solution in QCD-like theories without scalar fields. However, all of these theories have instantons and their finite-$T$ constituents known as instanton-dyons (or instanton-monopoles). The latter leads to semiclassical partition functions, which for ${\cal N} = 2,\,4$ theories were shown to be identical ("Poisson dual") to the partition function for monopoles. We show how, in a pure gauge theory, the semiclassical instanton-based partition function can also be Poisson-transformed into a partition function, interpreted as the one of moving and rotating monopoles.