BPS strings and the stability of the asymptotic Casimir law in adjoint flavor-symmetric YMH models

TL;DR

This paper studies a flavor-symmetric Yang-Mills-Higgs model with adjoint scalars, deriving BPS vortex solutions, and demonstrates that the model reproduces the Casimir law for string tension at large distances.

Contribution

It introduces BPS equations for vortex solutions in an adjoint scalar Yang-Mills-Higgs model and proves the model's ability to reproduce the asymptotic Casimir law for string tension.

Findings

Antisymmetric representations have lowest energy for given N-ality.

The model reproduces the Casimir law for string tension at large distances.

BPS vortex solutions are explicitly constructed and analyzed.

Abstract

We investigate an effective flavor-symmetric Yang-Mills-Higgs model with $N^2-1$ adjoint scalar fields. We find a set of BPS equations that provide vortex solutions and calculate their energies for arbitrary representations. We show that, for a given N-ality $k$, the energy of the corresponding antisymmetric representation is the lowest. This completes the proof that this model is able to reproduce a Casimir law for the string tension at asymptotic distances.