Generalized complex geometry and the Poisson Sigma Model

TL;DR

This paper explores how the supersymmetric Poisson Sigma model can realize generalized complex geometry on the worldsheet, revealing conditions for supersymmetry and new relations involving almost complex structures.

Contribution

It identifies specific relations among Poisson structures necessary for supersymmetry and uncovers new almost complex structure relations not directly linked to generalized complex structures.

Findings

Supersymmetric Poisson Sigma model can realize generalized complex geometry.

Certain Poisson structure relations are required for N=(2,1) or N=(2,2) supersymmetry.

Additional almost complex structures have relations with no immediate geometric interpretation.

Abstract

The supersymmetric Poisson Sigma model is studied as a possible worldsheet realization of generalized complex geometry. Generalized complex structures alone do not guarantee non-manifest N=(2,1) or N=(2,2) supersymmetry, but a certain relation among the different Poisson structures is needed. Moreover, important relations of an additional almost complex structure are found, which have no immediate interpretation in terms of generalized complex structures.