标题： 例外几何中的曲率层次 显示英文标题

标题： The Hierarchy of Curvatures in Exceptional Geometry

摘要： 尽管在描述超引力约化和背景方面取得了显著成功，广义几何和相关的例外场论仍然缺乏微分几何的基本对象，即黎曼张量。 我们解释说，为了构造这样的张量，需要一个迄今为止被忽视的连接层次结构。 它们通过从规范超引力的张量层次结构中已知的更高表示来补充自旋连接。 除了解决一个重要的概念性问题，这个想法还允许定义并显式构造广义齐性空间。 它们是广义U对偶性的基础结构，接受一致截断，并为具有非平凡广义结构群的通量紧化提供了大量新的背景。 显示英文摘要

摘要： Despite remarkable success in describing supergravity reductions and backgrounds, generalized geometry and the closely related exceptional field theory are still lacking a fundamental object of differential geometry, the Riemann tensor. We explain that to construct such a tensor, an as of yet overlooked hierarchy of connections is required. They complement the spin connection with higher representations known from the tensor hierarchy of gauged supergravities. In addition to solving an important conceptual problem, this idea allows to define and explicitly construct generalized homogeneous spaces. They are the underlying structures of generalized U-duality, admit consistent truncations and provide a huge class of new backgrounds for flux compactifications with non-trivial generalized structure groups.