Sigma models with off-shell N=(4,4) supersymmetry and noncommuting complex structures

TL;DR

This paper investigates the geometric conditions for extended off-shell N=(4,4) supersymmetry in semichiral sigma models, revealing new structures related to Yano f-structures and bi-hypercomplex geometry.

Contribution

It identifies conditions for off-shell N=(4,4) supersymmetry in semichiral sigma models and relates new geometric structures to known hypercomplex structures.

Findings

Some models exhibit additional off-shell supersymmetry.

The (4,4) supersymmetry induces structures described by Yano f-structures.

On-shell, these structures relate to bi-hypercomplex geometries.

Abstract

We describe the conditions for extra supersymmetry in N=(2,2) supersymmetric nonlinear sigma models written in terms of semichiral superfields. We find that some of these models have additional off-shell supersymmetry. The (4,4) supersymmetry introduces geometrical structures on the target-space which are conveniently described in terms of Yano f-structures and Magri-Morosi concomitants. On-shell, we relate the new structures to the known bi-hypercomplex structures.