Ensemble of Vortex Loops in the Abelian-Projected SU(3)-Gluodynamics

TL;DR

This paper investigates a grand canonical ensemble of vortex loops in the Abelian-projected SU(3) gluodynamics, revealing the interactions between two gases of vortex loops and deriving representations for the partition function.

Contribution

It introduces a novel analysis of vortex loop interactions in SU(3) gluodynamics and derives new integral representations for the partition function.

Findings

Derived two alternative representations for the partition function.

Evaluated correlators of vortex loops in the low-energy limit.

Identified the interaction effects between two vortex loop gases.

Abstract

Grand canonical ensemble of small vortex loops emerging in the London limit of the effective Abelian-projected theory of the SU(3)-gluodynamics is investigated in the dilute gas approximation. An essential difference of this system from the SU(2)-case is the presence of two interacting gases of vortex loops. Two alternative representations for the partition function of such a grand canonical ensemble are derived, and one of them, which is a representation in terms of the integrals over vortex loops, is employed for the evaluation of the correlators of both kinds of loops in the low-energy limit.