Extended Geometry and String Theory

我们将以仿埃尔米特几何及其推广的语言探索双重和扩展几何的全局公式，类似于广义几何的相关发展。特别是，我们将发展的概念，杂合para-Hermitian流形和它的关系，杂合双场论和杂合柯朗代数胚，以及推广到扩展几何基础的特殊场论紧化的M-理论和它们的关系，以更高的代数胚的特殊广义几何。在所有的推广中，我们将计算出从二重几何的研究中已知的DFT代数体的相应概念，以及控制其自同构的相关sigma模型和同伦代数的性质。

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.