Quark Potentials in the Higgs Phase of Large N Supersymmetric Yang-Mills Theories

TL;DR

This paper analyzes the quark potential in large N supersymmetric Yang-Mills theories with symmetry breaking, revealing how the potential and stability of states depend on distance and W-particle interactions.

Contribution

It provides a detailed computation of quark potentials in broken supersymmetric gauge theories, highlighting the transition from Coulomb to linear potential and the instability caused by W-particle production.

Findings

At short distances, the potential is Coulombic, falling off as 1/L.

Long-distance interactions involve complex states with W-particles.

Flux tubes become unstable due to W-particle production at small separations.

Abstract

We compute, in the large N limit, the quark potential for ${\cal N}=4$ supersymmetric SU(N) Yang-Mills theory broken to $SU(N_1) \times SU(N_2)$. At short distances the quarks see only the unbroken gauge symmetry and have an attractive potential that falls off as 1/L. At longer distances the interquark interaction is sensitive to the symmetry breaking, and other QCD states appear. These states correspond to combinations of the quark-antiquark pair with some number of W-particles. If there is one or more W-particles then this state is unstable because of the coulomb interaction between the W-particles and between the W's and the quarks. As L is decreased the W-particles delocalize and these coulomb branches merge onto a branch with a linear potential. The quarks on this branch see the unbroken gauge group, but the flux tube is unstable to the production of W-particles.