Twisted N=2 Supersymmetry with Central Charge and Equivariant Cohomology

TL;DR

This paper develops an equivariant extension of the Thom form within the Mathai-Quillen formalism to construct topological quantum field theories related to twisted N=2 supersymmetry with a central charge, applied to sigma models and monopoles.

Contribution

It introduces an equivariant Thom form extension that connects topological quantum field theories with twisted N=2 supersymmetry including a central charge.

Findings

Constructed equivariant Thom form in Mathai-Quillen formalism.

Formulated topological quantum field theories for twisted N=2 supersymmetry.

Analyzed cases of sigma models and non-abelian monopoles.

Abstract

We present an equivariant extension of the Thom form with respect to a vector field action, in the framework of the Mathai-Quillen formalism. The associated Topological Quantum Field Theories correspond to twisted $N=2$ supersymmetric theories with a central charge. We analyze in detail two different cases: topological sigma models and non-abelian monopoles on four-manifolds.