Yano F structures and extended Supersymmetry

DOI10.1007/JHEP10(2022)115arXiv2207.11780MaRDI QIDQ6405870

Publication date: 24 July 2022

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.

Mathematics Subject Classification ID

Supersymmetric field theories in quantum mechanics (81T60) Applications of differential geometry to physics (53Z05) Hyper-Kähler and quaternionic Kähler geometry, ``special geometry (53C26) Generalized geometries (à la Hitchin) (53D18)

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