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.
Highlights
The chromoelectric flux tube between external quarks in SUðNÞ Yang-Mills (YM) theory [1,2,3,4,5,6] has many interesting properties
The lattice string tension σIðDÞ, derived from the Wilson loop average hWCi,1 scales with the quadratic Casimir C2ðDÞ of the SUðNÞ quark representation Dð·Þ, see Ref. [2]
We will be mainly interested in the behavior at asymptotic distances, where the string tension is known to depend only on the N-ality of Dð·Þ [7]
Summary
The chromoelectric flux tube between external quarks in SUðNÞ Yang-Mills (YM) theory [1,2,3,4,5,6] has many interesting properties. The lattice string tension σIðDÞ, derived from the Wilson loop average hWCi, scales with the quadratic Casimir C2ðDÞ of the SUðNÞ quark representation Dð·Þ, see Ref. In the adjoint flavor-symmetric model, the tension of the infinite k-A string scales with the quadratic Casimir [9], which is compatible with the second possibility In this context, in order to establish the asymptotic Casimir scaling law one must show that this is the lowest tension among the irreps with N-ality k. [31], only for SUð2Þ, when the Higgs fields are in the adjoint At this point, we will close an ansatz for a string carrying any weight of SUðNÞ showing that, for a given N-ality k, the tension corresponding to the k-antisymmetric representation is the lowest
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