Revisiting Critical Vortices in Three-Dimensional SQED

TL;DR

This paper investigates quantum corrections to the mass and central charge of supersymmetric vortices in 2+1 dimensions, demonstrating preservation of BPS saturation and revealing fractionalization of global charges through detailed renormalization analysis.

Contribution

It introduces a novel approach to analyze quantum corrections in 2+1D N=2 SQED vortices, showing mass and charge renormalization and fractionalization effects.

Findings

Mass and central charge receive equal quantum corrections.

BPS saturation is preserved at the quantum level.

Fractionalization of the global U(1) charge to 1/2 for minimal vortices.

Abstract

We consider renormalization of the central charge and the mass of the ${\cal N}=2$ supersymmetric Abelian vortices in 2+1 dimensions. We obtain ${\cal N}=2$ supersymmetric theory in 2+1 dimensions by dimensionally reducing the ${\cal N}=1$ SQED 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 BPS 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.