Contrasting confinement in superQCD and superconductors

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The vacuum of supersymmetric gauge theories (SQCD) with N = 2 softly broken to N = 1 resembles that of a BCS superconductor in that it has a condensate which collimates flux into vortices, leading to confinement. We embed the SQCD vortex into the BCS theory by identifying the N = 1 vector multiplet mass and lightest massive chiral multiplet mass with the Fermi velocity divided by the London penetration depth and correlation length respectively. We claim that the magnetic flux in the vortex core exceeds the BCS critical magnetic field. As a result the superconductor undergoes a first order phase transition and ceases to superconduct, while the SQCD theory undergoes no such phase transition and so no longer agrees with the BCS theory. We consider more general superpotentials which are polynomial in the chiral multiplets and find that, at tree level, BCS vortices (equivalently type II superconductivity) exist only when the superpotential perturbation is at least quadratic in the fundamental chiral multiplets and at least linear in the adjoint chiral multiplets, in which case there is no N = 2 supersymmetry in the ultraviolet.