A three-dimensional scalar field theory model of center vortices and its relation to k-string tensions

TL;DR

This paper models center vortices in 3D SU(N) gauge theory using scalar fields, providing a new approach to understanding k-string tensions through vortex dynamics and their relation to gauge theory quantum solitons.

Contribution

It introduces a scalar field theory model of center vortices that captures their merging, dissociation, and recombination, offering a novel method to analyze k-string tensions at large N.

Findings

Vortex dynamics suggest linear k-string tensions for small k/N ratios.

The scalar field model connects vortex configurations with gauge theory quantum solitons.

A simplified molecular dynamics approximation supports expected tension behaviors.

Abstract

In d=3 SU(N) gauge theory, we study a scalar field theory model of center vortices that furnishes an approach to the determination of so-called k-string tensions. This model is constructed from string-like quantum solitons introduced previously, and exploits the well-known relation between string partition functions and scalar field theories in d=3. Center vortices corresponding to magnetic flux J (in units of 2\pi /N) are composites of J elementary J=1 constituent vortices that come in N-1 types, with repulsion between like constituents and attraction between unlike constituents. The scalar field theory involves N scalar fields \phi_i (one of which is eliminated) that can merge, dissociate, and recombine while conserving flux mod N. The properties of these fields are deduced directly from the corresponding gauge-theory quantum solitons. Every vacuum Feynman graph of the theory corresponds to a real-space configuration of center vortices. We study qualitatively the problem of k-string tensions at large N, whose solution is far from obvious in center-vortex language. We construct a simplified dynamical picture of constituent-vortex merging, dissociation, and recombination, which allows in principle for the determination of vortex areal densities and k-string tensions. This picture involves point-like "molecules" (cross-sections of center vortices) made of constituent "atoms" that combine and disassociate dynamically in a d=2 test plane . The vortices evolve in a Euclidean "time" which is the location of the test plane along an axis perpendicular to the plane. A simple approximation to the molecular dynamics is compatible with k-string tensions that are linear in k for k<< N, as naively expected.