Yano F structures and extended Supersymmetry

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.

25 pages V2: Nomenclature and one equation corrected

References in corpus (3)

• Nonabelian Generalized Gauge Multiplets
• All $(4,0)$: Sigma Models with $(4,0)$ Off-Shell Supersymmetry
• Extended supersymmetry of semichiral sigma model in 4D