Supersymmetric Gauge Theories, Vortices and Equivariant Cohomology

TL;DR

This paper constructs supersymmetric gauge theories with matter, derives scalar potentials, and shows their Euclidean actions are bounded by topological charges related to equivariant Kahler forms, generalizing vortex solutions.

Contribution

It introduces new supersymmetric gauge theories coupled to sigma models, derives scalar potentials, and establishes topological bounds on Euclidean actions involving equivariant cohomology.

Findings

Euclidean actions bounded by topological charges involving equivariant Kahler forms

Generalization of vortex solutions to supersymmetric gauge theories in various dimensions

Explicit construction of supersymmetric actions with scalar potentials

Abstract

We construct actions for (p,0)- and (p,1)- supersymmetric, 1 <= p <= 4, two-dimensional gauge theories coupled to non-linear sigma model matter with a Wess-Zumino term. We derive the scalar potential for a large class of these models. We then show that the Euclidean actions of the (2,0) and (4,0)-supersymmetric models without Wess-Zumino terms are bounded by topological charges which involve the equivariant extensions of the Kahler forms of the sigma model target spaces evaluated on the two-dimensional spacetime. We give similar bounds for Euclidean actions of appropriate gauge theories coupled to non-linear sigma model matter in higher spacetime dimensions which now involve the equivariant extensions of the Kahler forms of the sigma model target spaces and the second Chern character of gauge fields. The BPS configurations are generalisations of abelian and non-abelian vortices.