The Topological B-model on a Mini-Supertwistor Space and Supersymmetric Bogomolny Monopole Equations

TL;DR

This paper explores the twistor correspondence between a topological B-model on mini-supertwistor space and supersymmetric Bogomolny equations, introducing new geometric insights and solution techniques for three-dimensional super Yang-Mills theories.

Contribution

It establishes a twistor correspondence linking a holomorphic Chern-Simons theory on supertwistor space to supersymmetric Bogomolny equations, including deformations that introduce mass terms.

Findings

Developed a twistor framework for supersymmetric Bogomolny equations

Constructed action functionals for involved theories

Presented solution-generating techniques and examples

Abstract

In the recent paper hep-th/0502076, it was argued that the open topological B-model whose target space is a complex (2|4)-dimensional mini-supertwistor space with D3- and D1-branes added corresponds to a super Yang-Mills theory in three dimensions. Without the D1-branes, this topological B-model is equivalent to a dimensionally reduced holomorphic Chern-Simons theory. Identifying the latter with a holomorphic BF-type theory, we describe a twistor correspondence between this theory and a supersymmetric Bogomolny model on R^3. The connecting link in this correspondence is a partially holomorphic Chern-Simons theory on a Cauchy-Riemann supermanifold which is a real one-dimensional fibration over the mini-supertwistor space. Along the way of proving this twistor correspondence, we review the necessary basic geometric notions and construct action functionals for the involved theories. Furthermore, we discuss the geometric aspect of a recently proposed deformation of the mini-supertwistor space, which gives rise to mass terms in the supersymmetric Bogomolny equations. Eventually, we present solution generating techniques based on the developed twistorial description together with some examples and comment briefly on a twistor correspondence for super Yang-Mills theory in three dimensions.