Structure of center-vortex matter in SU(4) Yang-Mills theory

TL;DR

This study explores the detailed structure of center vortices in SU(4) Yang-Mills theory, revealing new types of doubly charged vortices and their statistical properties, advancing understanding of non-Abelian gauge theories.

Contribution

First analysis of center vortex structures in SU(4) Yang-Mills theory, including classification and statistical characterization of doubly charged vortices and their chains.

Findings

Doubly charged vortices are physically distinct from elementary vortices in SU(4).

Vortex chains are shorter but more common than convergences, acting as extended monopoles.

Vortex chain lengths follow an exponential distribution, indicating a constant splitting probability.

Abstract

The structure of center vortices is studied in SU(4) Yang-Mills theory for the first time to illuminate the interplay between elementary (center charge $\pm 1$) and doubly charged vortices. Unlike in SU(3), where charge $+2$ vortices are simply elementary vortices with reversed orientations in spacetime, these possibilities are physically distinct in SU(4). Visualizations of the vortex structure in three-dimensional slices reveal the various ways in which doubly charged objects manifest, as the convergence and matching of elementary vortices or as isolated doubly charged loops. An algorithm is described to classify every doubly charged chain as one of these three types. A collection of vortex statistics is considered to quantify the vortex structure. Many of these pertain to the novel doubly charged objects, including their relative proportions and chain lengths, which are analyzed to highlight the differences between each chain type. Three different lattice spacings are employed to investigate the approach to the continuum limit. Vortex matching chains are found to be shorter on average but also more prevalent than vortex convergences, ascribed to their interpretation as extended center monopoles. In addition, the lengths of both vortex convergences and vortex matchings are observed to follow an exponential distribution, allowing the introduction of a constant probability for a doubly charged chain to split into two elementary vortices as it propagates. Combined, these findings provide a characterization of the vortices that comprise center-vortex structures in SU(4) Yang-Mills theory.