BPS strings and the stability of the asymptotic Casimir law in adjoint flavor-symmetric Yang-Mills-Higgs models

We investigate an effective flavor-symmetric Yang-Mills-Higgs model with ${N}^{2}\ensuremath{-}1$ adjoint scalar fields. We find a set of Bogomol'nyi-Prasad-Sommerfield 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.