论文标题
Hyperkähler，Bi-HyperComplex，广义Hyperkähler结构和T-偶数
Hyperkähler, Bi-hypercomplex, Generalized Hyperkähler Structures and T-duality
论文作者
论文摘要
我们在二维$ \ Mathcal {n} =（2,2）$ sigma模型中调查了T-偶数，复杂和双甲状化结构之间的全面关系。 Bi-Hermitian结构$（J _+，J _-）$嵌入了广义的Kähler结构$（\ Mathcal {J} _+，\ Mathcal {J} _-）$被组织到Tri-complex编号的代数中。我们新写下了Buscher规则的类似物，通过该规则，Bi-Hermitian和Kähler结构的T偶对变化显而易见。我们还研究了$ \ Mathcal {n} =（4,4）$理论的Bi-Hypercomplex和Hyperkähler案例。它们在广义的Hyperkähller结构中以T-偶的协变方式表示，并形成了分裂的Bi-quathnion代数。作为一个具体的例子，我们显示了Kk-konopole（Taub-nut空间）的HyperKähler结构与H-Monopole（涂抹的NS5-Brane）的Bi-HyperComplex结构之间的显式T-偶尔关系。利用此结果，我们评论了这些几何形状中的世界单曲Instantons的T偶尔关系。
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.
