Yano F structures and extended Supersymmetry

TL;DR

This paper explores how extended supersymmetry in a symplectic sigma model induces a geometric structure involving Yano F structures on a para-hermitian manifold, linking supersymmetry with advanced geometric frameworks.

Contribution

It demonstrates the emergence of Yano F structures from extended supersymmetry on (2,2) semichiral superfields and relates this to generalized geometry and bi-quaternionic structures.

Findings

Extended supersymmetry induces Yano F structures on the doubled tangent bundle.

Closure and invariance of the algebra are established within this geometric framework.

The formulation connects to generalized geometry and can be applied to other models.

Abstract

It is shown how extended supersymmetry realised directly on the (2,2) semichiral superfields of a symplectic sigma model gives rise to a geometry on the doubled tangent bundle consisting of two Yano F structures on an almost para-hermitian manifold. Closure of the algebra and invariance of the action is discussed in this framework and integrability of the F structures is defined and shown to hold. The reduction to the usual (1, 1) sigma model description and identification with the bi-quaternionic set of complex structures and their properties is elucidated. The F structure formulation should be applicable to many other models and will have an equivalent formulation in Generalised Geometry.