arXiv 1603.030952016-03hep-thmath.AGmath.DG

四维几何U形折叠

Geometric U-folds in four dimensions

C. I. Lazaroiu, C. S. Shahbazi

备注：: 10 pages. Conclusions and references added. Exposition improved
发表信息：: J. Phys. A: Math. Theor. 51 015207, 2017
DOI：: 10.1088/1751-8121/aa9665

摘要：

我们描述了一个几何U-折叠的建设兼容的非平凡的扩展的四维扩展超引力的整体制定的可微自旋流形。几何U形折叠的拓扑结构取决于某些扁平纤维束，这些纤维束编码了超重力场是如何整体粘合在一起的。我们证明了这种类型的光滑非平凡U-折叠只存在于标量和时空流形都具有非平凡基本群的理论中，此外，解的标量映射是同伦非平凡的。与弦论的一致性要求光滑几何U-折叠可以用有效离散U-对偶群的子群来粘合，这意味着这样的解的标量流形的基本群必须是后者的子群。我们构造了简单的几何U-折叠的例子，在一个推广的轴子-介子模型的$\mathcal{N}=2$超引力耦合到一个单一的矢量多重态，其标量流形是一个一般的非紧黎曼曲面的亏格至少有两个赋予其均匀化度量。我们还讨论了几何U-折叠与定义在标量流形上的平坦联络的模空间之间的关系，其中涉及到一些文献中没有研究过的特征簇。

英文摘要：

We describe a construction of geometric U-folds compatible with a non-trivial extension of the global formulation of four-dimensional extended supergravity on a differentiable spin manifold. The topology of geometric U-folds depends on certain flat fiber bundles which encode how supergravity fields are globally glued together. We show that smooth non-trivial U-folds of this type can exist only in theories where both the scalar and space-time manifolds have non-trivial fundamental group and in addition, the scalar map of the solution is homotopically non-trivial. Consistency with string theory requires smooth geometric U-folds to be glued using subgroups of the effective discrete U-duality group, implying that the fundamental group of the scalar manifold of such solutions must be a subgroup of the latter. We construct simple examples of geometric U-folds in a generalization of the axion-dilaton model of $\mathcal{N}=2$ supergravity coupled to a single vector multiplet, whose scalar manifold is a generally non-compact Riemann surface of genus at least two endowed with its uniformizing metric. We also discuss the relation between geometric U-folds and a moduli space of flat connections defined on the scalar manifold, which involves certain character varieties not studied in the literature.

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英文摘要：

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