Quantum corrections to solitons and BPS saturation

TL;DR

This paper reviews a decade of research on quantum corrections to soliton masses and charges in supersymmetric theories, highlighting new anomaly-like contributions and the use of specialized regularization techniques.

Contribution

It introduces novel anomaly-like contributions and renormalization methods necessary for BPS saturation in supersymmetric solitons.

Findings

Identification of anomaly-like contributions to central charge Z

Role of classical winding and surface terms in quantum corrections

Use of modified dimensional regularization preserving supersymmetry

Abstract

We review our work of the past decade on one-loop quantum corrections to the mass M and central charge Z of solitons in supersymmetric field theories: the kink, the vortex, and the monopoles (focussing on the kink and the monopoles here). In each case a new feature was needed to obtain BPS saturation: a new anomaly-like contribution to Z for the kink and the N=2 monopole, the effect of classical winding of the quantum vortex contributing to Z, surface terms contributing to M of the N=4 monopole and to Z of the N=2 and N=4 monopoles, and composite operator renormalization for the currents of the "finite" N=4 model. We use dimensional regularization, modified to preserve susy and be applicable to solitons, and suitable renormalization conditions. In the mode expansion of bosonic and fermionic quantum fields, zero modes appear then as massless nonzero modes.