Revisiting critical vortices in three-dimensional supersymmetric QED

We consider renormalization of the central charge and the mass of the N=2 supersymmetric Abelian vortices in 2+1 dimensions. We obtain N=2 supersymmetric theory in 2+1 dimensions by dimensionally reducing the N=1 supersymmetric QED in 3+1 dimensions with two chiral fields carrying opposite charges. Then we introduce a mass for one of the matter multiplets without breaking N=2 supersymmetry. This massive multiplet is viewed as a regulator in the large mass limit. We show that the mass and the central charge of the vortex get the same nonvanishing quantum corrections, which preserves Bogomol'nyi-Prasad-Sommerfield saturation at the quantum level. Comparison with the operator form of the central extension exhibits fractionalization of a global U(1) charge; it becomes ±1/2 for the minimal vortex. The very fact of the mass and charge renormalization is due to a "reflection" of an unbalanced number of the fermion and boson zero modes on the vortex in the regulator sector.