ELLIPTIC MONOPOLES AND (4,0)-SUPERSYMMETRIC SIGMA MODELS WITH TORSION

TL;DR

This paper constructs specific (4,0)-supersymmetric sigma models with torsion on four-manifolds, revealing their metric couplings relate to magnetic monopoles on three-spheres and analyzing their global structures.

Contribution

It explicitly constructs (4,0)-supersymmetric sigma models with torsion, linking metric couplings to magnetic monopoles and analyzing their global properties.

Findings

Metric couplings from magnetic monopoles on S^3

Only the SU(2)×U(1) WZW model is non-singular with torsion

Global structure analysis of SO(3)-invariant metrics

Abstract

We explicitly construct the metric and torsion couplings of two-dimensional (4,0)-super\-sym\-metric sigma models with target space a four-manifold that are invariant under a $U(1)$ symmetry generated by a tri-holomorphic Killing vector field that leaves in addition the torsion invariant. We show that the metric couplings arise from magnetic monopoles on the three-sphere which is the space of orbits of the group action generated by the tri-holomorphic Killing vector field on the sigma model target manifold. We also examine the global structure of a subclass of these metrics that are in addition $SO(3)$-invariant and find that the only non-singular one, for models with non-zero torsion, is that of $SU(2)\times U(1)$ WZW model.