Poisson geometry of sigma models with extended supersymmetry

TL;DR

This paper explores how extended supersymmetry in N=(2,2) sigma models necessitates the target space to possess two distinct Poisson structures, highlighting the role of Poisson geometry in such models.

Contribution

It demonstrates that N=(2,2) supersymmetry imposes the presence of two Poisson structures on the target manifold, revealing a geometric characteristic of extended supersymmetric sigma models.

Findings

Target manifolds must have two Poisson structures for N=(2,2) supersymmetry.

Poisson geometry is fundamental in extended supersymmetric sigma models.

The structure distinguishes models with extended supersymmetry from simpler cases.

Abstract

We consider a general N=(2,2) non-linear sigma model with a torsion. We show that the consistency of N=(2,2) supersymmetry implies that the target manifold is necessary equipped with two (in general, different) Poisson structures. Finally we argue that the Poisson geometry of the target space is a characteristic feature of the sigma models with extended supersymmetry.