Yano F structures and extended supersymmetry

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.

Automated summary

This paper investigates 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. The closure of the algebra and invariance of the action are discussed within this framework, and the integrability of the F structures is defined and shown to hold. The paper also explores the reduction to the usual (1,1) sigma model description and establishes its identification with the bi-quaternionic set of complex structures and their properties. The F structure formulation has potential applications in many other models and can be equivalently formulated in Generalised Geometry.