The infrared Yang-Mills wave functional due to percolating center vortices

TL;DR

This paper develops a vacuum wave functional model based on correlated center vortices in SU(N) Yang-Mills theory, capturing infrared properties and demonstrating Casimir scaling of the string tension.

Contribution

It introduces a novel wave functional incorporating vortex correlations, stiffness, and monopoles, providing a new effective description of the infrared Yang-Mills vacuum.

Findings

Effective potential exhibits only center symmetry, which is spontaneously broken in the vortex condensed phase.

Wilson loop averages are approximated by solitonic saddle points around minimal surfaces.

Asymptotic string tension shows Casimir scaling behavior.

Abstract

Inspired by the center-vortex dominance in the infrared sector of $SU(N)$ Yang-Mills theory observed on the lattice, we propose a vacuum wave functional localized on an ensemble of correlated center vortices endowed with stiffness and magnetic monopoles that change the orientation of the vortex flux. In the electric-field representation, this wave functional becomes an effective partition function for N complex scalar fields. The inclusion of both oriented and non-oriented vortices as well as so-called N-vortex matchings leads to an effective potential that has only a center symmetry left. In the center-vortex condensed phase, this symmetry is spontaneously broken. In this case, the Wilson loop average can be approximated by a solitonic saddle-point localized around the minimal surface. The asymptotic string tension thus obtained displays Casimir scaling.