超Kähler、双超复形、广义超Kähler结构和T-对偶
Hyperkähler, Bi-hypercomplex, Generalized Hyperkähler Structures and T-duality
摘要：
研究了二维$\mathcal{N} =(2,2)$西格玛模型中T-对偶、复结构和双厄米结构$(J_+, J_-)$之间的关系.嵌入在广义Kähler结构$(\mathcal{J}_+,\mathcal{J}_-)$中的双厄米结构$(J_+,J_-)$被组织成三复数的代数。我们新写下来的Buscher规则的T-对偶变换的双厄米和Kähler结构是显而易见的类似物。我们还研究了$\mathcal{N} = (4,4)$理论中的双超复形和超kähler情形。它们以T-对偶协变的形式表示在广义超Kähler结构中，并形成分裂双四元数代数。作为一个具体的例子，我们给出了KK-流形（Taub-NUT空间）的超kähler结构与H-流形（涂抹NS 5-膜）的双超复结构之间的显式T-对偶关系.利用这一结果，我们评论的T-对偶关系的世界片瞬子在这些几何。
英文摘要：
We investigate comprehensive relations among T-duality, complex and bi-hermitian structures $(J_+, J_-)$ in two-dimensional $\mathcal{N} =(2,2)$ sigma models with/without twisted chiral multiplets. The bi-hermitian structures $(J_+,J_-)$ embedded in generalized Kähler structures $(\mathcal{J}_+,\mathcal{J}_-)$ are organized into the algebra of the tri-complex numbers. We newly write down an analogue of the Buscher rule by which the T-duality transformation of the bi-hermitian and Kähler structures are apparent. We also study the bi-hypercomplex and hyperkähler cases in $\mathcal{N} = (4,4)$ theories. They are expressed, as a T-duality covariant fashion, in the generalized hyperkähler structures and form the split-bi-quaternion algebras. As a concrete example, we show the explicit T-duality relation between the hyperkähler structures of the KK-monopole (Taub-NUT space) and the bi-hypercomplex structures of the H-monopole (smeared NS5-brane). Utilizing this result, we comment on a T-duality relation for the worldsheet instantons in these geometries.
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