Type I Non-Abelian Superconductors in Supersymmetric Gauge Theories

Abstract

Non-BPS non-Abelian vortices with CP^1 internal moduli space are studied in an N=2 supersymmetric U(1) x SU(2) gauge theory with softly breaking adjoint mass terms. For generic internal orientations the classical force between two vortices can be attractive or repulsive. On the other hand, the mass of the scalars in the theory is always less than that of the vector bosons; also, the force between two vortices with the same CP^1 orientation is always attractive: for these reasons we interpret our model as a non-Abelian generalization of type I superconductors. We compute the effective potential in the limit of two well separated vortices. It is a function of the distance and of the relative colour-flavour orientation of the two vortices; in this limit we find an effective description in terms of two interacting CP^1 sigma models. In the limit of two coincident vortices we find two different solutions with the same topological winding and, for generic values of the parameters, different tensions. One of the two solutions is described by a CP^1 effective sigma model, while the other is just an Abelian vortex without internal degrees of freedom. For generic values of the parameters, one of the two solutions is metastable, while there are evidences that the other one is truly stable.

35 pages, 8 figures. v2: fixed typos and added small comments, v3 removed an unecessary figure

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• Fractional Vortices and Lumps
• Non-Abelian Monopoles in the Higgs Phase
• Multiple Layer Structure of Non-Abelian Vortex
• Non-Abelian Global Vortices
• On the Stability of Non-Abelian Semi-local Vortices
• Non-Abelian monopole-vortex complex
• Monopole-vortex complex at large distances and nonAbelian duality
• The holographic vortex lattice using the circular cell method
• Dynamics of global and local vortices with orientational moduli
• Monopole-vortex complex in a theta vacuum