The Generalised Complex Geometry of $(p,q)$ Hermitian Geometries

Abstract

We define $(p,q)$ hermitian geometry as the target space geometry of the two dimensional $(p,q)$ supersymmetric sigma model. This includes generalised Kähler geometry for $(2,2)$, generalised hyperkähler geometry for $(4,2)$, strong Kähler with torsion geometry for $(2,1)$ and strong hyperkähler with torsion geometry for $(4,1)$. We provide a generalised complex geometry formulation of hermitian geometry, generalising Gualtieri's formulation of the $(2,2)$ case. Our formulation involves a chiral version of generalised complex structure and we provide explicit formulae for the map to generalised geometry.

20 pages

References in corpus (3)

• Linearizing Generalized Kahler Geometry
• All $(4,0)$: Sigma Models with $(4,0)$ Off-Shell Supersymmetry
• All $(4,1)$: Sigma Models with $(4,q)$ Off-Shell Supersymmetry

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