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The Generalised Complex Geometry of (p, q) Hermitian Geometries
Communications in Mathematical Physics ( IF 2.2 ) Pub Date : 2019-06-24 , DOI: 10.1007/s00220-019-03488-3
Christopher Hull , Ulf Lindström

We define $(p,q)$ hermitian geometry as the target space geometry of the two dimensional $(p,q)$ supersymmetric sigma model. This includes generalised Kahler geometry for $(2,2)$, generalised hyperkahler geometry for $(4,2)$, strong Kahler with torsion geometry for $(2,1)$ and strong hyperkahler 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.

中文翻译:

(p, q) Hermitian 几何的广义复几何

我们将 $(p,q)$ 厄密几何定义为二维 $(p,q)$ 超对称 sigma 模型的目标空间几何。这包括 $(2,2)$ 的广义 Kahler 几何、$(4,2)$ 的广义超级卡勒几何、$(2,1)$ 具有扭转几何的强 Kahler 和 $(4, 1)$。我们提供了厄密几何的广义复杂几何公式,概括了 $(2,2)$ 情况的 Gualtieri 公式。我们的公式涉及广义复杂结构的手性版本,并且我们提供了映射到广义几何的明确公式。
更新日期:2019-06-24
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