k-strings and baryon vertices in SU(N) gauge theories

TL;DR

This paper explores the conditions under which the sine law for k-string tension leads to spontaneous breaking of Z_N symmetry in SU(N) gauge theories and similar systems, analyzing baryon vertices and stability.

Contribution

It demonstrates that the sine law for k-string tension determines the critical threshold for Z_N symmetry breaking in gauge theories with baryon vertices.

Findings

Sine law for k-string tension signals Z_N symmetry breaking threshold

Applicable to SU(N) and other gauge systems with stable k-strings

Provides examples illustrating the theoretical results

Abstract

It is pointed out that the sine law for the k-string tension emerges as the critical threshold below which the spatial Z_N symmetry of the static baryon potential is spontaneously broken. This result applies not only to SU(N) gauge theories, but to any gauge system with stable k-strings admitting a baryon vertex made with N sources in the fundamental representation. Some simple examples are worked out.