Nonvanishing quantum corrections to the mass and central charge of the N=2 vortex and BPS saturation

TL;DR

This paper calculates one-loop quantum corrections to the mass and central charge of the N=2 vortex in 2+1 dimensions, showing they are nonvanishing but still satisfy BPS saturation due to supersymmetry.

Contribution

It demonstrates that quantum corrections to the N=2 vortex's mass and central charge are nonzero yet equal, confirming BPS saturation with a corrected understanding of multiplet structure.

Findings

Both mass and central charge receive nonzero one-loop corrections.

Quantum corrections preserve BPS saturation by equality of mass and charge.

Corrects previous claims about degeneracy of short multiplets at quantum level.

Abstract

The one-loop quantum corrections to the mass and central charge of the N=2 vortex in 2+1 dimensions are determined using supersymmetry-preserving dimensional regularization by dimensional reduction of the corresponding N=1 model with Fayet-Iliopoulos term in 3+1 dimensions. Both the mass and the central charge turn out to have nonvanishing one-loop corrections which however are equal and thus saturate the Bogomolnyi bound. We explain BPS saturation by standard multiplet shortening arguments, correcting a previous claim in the literature postulating the presence of a second degenerate short multiplet at the quantum level.