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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 providevortex solutions and calculate their energies for arbitrary representations. Weshow that, for a given N-ality $k$, the energy of the correspondingantisymmetric representation is the lowest. This completes the proof that thismodel is able to reproduce a Casimir law for the string tension at asymptoticdistances.

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