Quantum corrections to the mass of the supersymmetric vortex

TL;DR

This paper calculates quantum corrections to the mass of a supersymmetric vortex in a 2+1 dimensional abelian Higgs model, using zeta function regularization and analyzing supersymmetry effects.

Contribution

It provides a detailed computation of quantum mass corrections for supersymmetric vortices, highlighting the role of boundary conditions and finite renormalization.

Findings

Quantum corrections arise from finite renormalization of couplings.

Remaining supersymmetry ensures isospectrality despite boundary condition violations.

The correction to vortex mass is explicitly calculated using zeta function regularization.

Abstract

We calculate quantum corrections to the mass of the vortex in N=2 supersymmetric abelian Higgs model in (2+1) dimensions. We put the system in a box and apply the zeta function regularization. The boundary conditions inevitably violate a part of the supersymmetries. Remaining supersymmetry is however enough to ensure isospectrality of relevant operators in bosonic and fermionic sectors. A non-zero correction to the mass of the vortex comes from finite renormalization of couplings.