Central charge and renormalization in supersymmetric theories with vortices

TL;DR

This paper investigates quantum aspects of vortices in 2+1D supersymmetric theories, showing no quantum anomaly in supertrace identities, and precisely determining vortex spectra at one loop with higher-order corrections for excitations.

Contribution

It demonstrates the absence of quantum anomalies in supertrace identities and provides an exact one-loop calculation of vortex spectra in supersymmetric theories.

Findings

No genuine quantum anomaly in supertrace identity.

Vortex spectrum is exactly determined at one loop.

Elementary excitation spectrum receives higher-order corrections.

Abstract

Some quantum features of vortices in supersymmetric theories in 1+2 dimensions are studied in a manifestly supersymmetric setting of the superfield formalism. A close examination of the supercurrent that accommodates the central charge and super-Poincare charges in a supermultiplet reveals that there is no genuine quantum anomaly in the supertrace identity and in the supercharge algebra, with the central-charge operator given by the bare Fayet-Iliopoulos term alone. The central charge and the vortex spectrum undergo renormalization on taking the expectation value of the central-charge operator. It is shown that the vortex spectrum is exactly determined at one loop while the spectrum of the elementary excitations receives higher-order corrections.