Yano F structures and extended Supersymmetry

2022-07-22

Authors: Ulf Lindström

Preprint number: UUITP-33/22

It is described 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 a parahermitian 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 described. The F structure formulation should be applicable to many other models and will have an equivalent formulation in Generalised Geometry.