BPS String Solutions in Non-Abelian Yang-Mills Theories and Confinement

TL;DR

This paper derives BPS string solutions in non-Abelian Yang-Mills theories, demonstrating their potential role in confinement by showing constant string tension and monopole confinement implications.

Contribution

It generalizes BPS string solutions to arbitrary semi-simple gauge groups and explores their properties within a supersymmetric gauge theory framework.

Findings

BPS Z_k-string solutions satisfy first order differential equations similar to U(1) case.

String tension remains constant across solutions.

Potential for linear confinement of monopoles is suggested.

Abstract

Starting from the bosonic part of N=2 Super QCD with a 'Seiberg-Witten' N=2 breaking mass term, we obtain string BPS conditions for arbitrary semi-simple gauge groups. We show that the vacuum structure is compatible with a symmetry breaking scheme which allows the existence of Z_k-strings and which has Spin(10) -> SU(5) x Z_2 as a particular case. We obtain BPS Z_k-string solutions and show that they satisfy the same first order differential equations as the BPS string for the U(1) case. We also show that the string tension is constant, which may cause a confining potential between monopoles increasing linearly with their distance.