Sigma-models having supermanifolds as target spaces

TL;DR

This paper investigates topological $A$-models with supermanifold target spaces, demonstrating their equivalence to models with purely bosonic targets under certain conditions, especially in toric geometry contexts.

Contribution

It proves the equivalence of $A$-models with supermanifold targets to those with reduced-dimensional manifolds, extending to toric supermanifolds for complete intersections.

Findings

Supermanifold $A$-models are equivalent to reduced models under certain conditions.

Complete intersection $A$-models in toric manifolds are equivalent to toric supermanifold models.

Results facilitate understanding of topological models with supergeometric target spaces.

Abstract

We study a topological sigma-model ($A$-model) in the case when the target space is an ($m_0|m_1$)-dimensional supermanifold. We prove under certain conditions that such a model is equivalent to an $A$-model having an ($m_0-m_1$)-dimensional manifold as a target space. We use this result to prove that in the case when the target space of $A$-model is a complete intersection in a toric manifold, this $A$-model is equivalent to an $A$-model having a toric supermanifold as a target space.