Extended Geometry and String Theory

我们将用拟厄米几何及其推广的语言来探讨二重几何和扩展几何的整体公式，类比于广义几何的相关发展。特别地，我们将发展异质拟厄米流形的概念及其与异质双场理论和异质Courant代数群的关系，以及在m理论的紧化中的例外场论基础上的扩展几何的推广及其与例外广义几何的高等代数群的关系。在所有的推广中，我们将从二重几何的研究中得出相应的DFT代数的概念，以及相关的sigma模型和控制其自同构的同伦代数的性质。

We will explore global formulations of doubled and extended geometry in the language of para-Hermitian geometry and its generalizations, in analogy to related developments in generalized geometry. In particular, we will develop the notion of heterotic para-Hermitian manifold and its relation to heterotic double field theory and heterotic Courant algebroids, as well as generalizations to extended geometries underlying exceptional field theories in compactifications of M-theory and their relations to the higher algebroids of exceptional generalized geometry. In all generalizations we will work out the corresponding notions of DFT algebroid known from investigations of doubled geometry, as well as the properties of related sigma-models and homotopy algebras which control their automorphisms.