Effective theory of the D = 3 center vortex ensemble

TL;DR

This paper develops an effective field theory for center vortex ensembles in 3D Yang-Mills theory, linking vortex properties to confinement mechanisms through a complex scalar field model.

Contribution

It introduces a novel effective theory mapping vortex ensembles to a U(1) symmetric scalar field, capturing confinement phenomena via tension and symmetry breaking.

Findings

Positive tension leads to perimeter law for Wilson loops.

Negative tension results in spontaneous symmetry breaking and area law.

The XY model with frustration describes quantum fluctuations of Goldstone modes.

Abstract

By means of lattice calculations, center vortices have been established as the infrared dominant gauge field configurations of Yang-Mills theory. In this work, we investigate an ensemble of center vortices in D = 3 Euclidean space-time dimension where they form closed flux loops. To account for the properties of center vortices detected on the lattice, they are equipped with tension, stiffness and a repulsive contact interaction. The ensemble of oriented center vortices is then mapped onto an effective theory of a complex scalar field with a U(1) symmetry. For a positive tension, small vortex loops are favoured and the Wilson loop displays a perimeter law while for a negative tension, large loops dominate the ensemble. In this case the U(1) symmetry of the effective scalar field theory is spontaneously broken and the Wilson loop shows an area law. To account for the large quantum fluctuations of the corresponding Goldstone modes, we use a lattice representation, which results in an XY model with frustration, for which we also study the Villain approximation.