Contrasting confinement in superQCD and superconductors

TL;DR

This paper explores the analogy between supersymmetric gauge theories and superconductors, analyzing vortex solutions and their validity within different theoretical frameworks, revealing conditions for type I and type II superconductivity.

Contribution

It establishes a detailed correspondence between SQCD vortices and BCS superconductors, highlighting the limitations of the Landau-Ginzburg approximation and conditions for different superconducting types.

Findings

SuperQCD vortices resemble BCS superconductor flux tubes.

Nonlocal effects limit the Landau-Ginzburg approximation validity.

Conditions for type I and type II superconductivity depend on superpotential form.

Abstract

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 coherence length respectively. Thus embedded the superconductivity is type I and so the vortex core is smaller than the coherence length. Therefore nonlocal effects (Pippard electrodynamics) imply that the vortex solution is beyond the range of validity of the Landau-Ginzburg approximation implicit in the gauge theory. In other words, the vortex solution contains gradients greater than those for which the BCS and gauge theory descriptions agree. We consider more general superpotentials which are polynomial in the chiral multiplets and find that, unless one adds a SUSY breaking sector, one obtains type II superconductivity 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.