Exceptional Calabi-Yau spaces: the geometry of backgrounds with flux
Exceptional Calabi-Yau spaces: the geometry of backgrounds with flux
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出色的卡拉比-丘空间：具有通量的背景几何
DOI：
10.1002/prop.201600109
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Ashmore A
中科院分区：
文献类型：
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作者：
Ashmore A
在本文中，我们定义了II型超引力和M理论中一般通量背景的卡-丘几何的类似物。我们证明了Killing旋量方程的解与广义几何中可积的、全局定义的结构一一对应。这种“特殊的卡-丘”几何是由两个广义对象确定的，它们参数化了超和向量多重自由度，并推广了传统的复、辛和超凯勒几何。超多重态和向量多重态结构的可积性条件都是通过将规范变换与复态同构的“广义复态同构群”的矩映射的消失给出的。我们给出了一些明确的例子，并讨论了结构的模空间的解决方案。然后，我们将我们的建设和通量背景保持8个超荷，类似的结构出现，最后讨论了类似的结构在广义几何。
In this paper we define the analogue of Calabi–Yau geometry for generic , flux backgrounds in type II supergravity and M‐theory. We show that solutions of the Killing spinor equations are in one‐to‐one correspondence with integrable, globally defined structures in generalised geometry. Such “exceptional Calabi–Yau” geometries are determined by two generalised objects that parametrise hyper‐ and vector‐multiplet degrees of freedom and generalise conventional complex, symplectic and hyper‐Kähler geometries. The integrability conditions for both hyper‐ and vector‐multiplet structures are given by the vanishing of moment maps for the “generalised diffeomorphism group” of diffeomorphisms combined with gauge transformations. We give a number of explicit examples and discuss the structure of the moduli spaces of solutions. We then extend our construction to and flux backgrounds preserving eight supercharges, where similar structures appear, and finally discuss the analogous structures in generalised geometry.