Geometrical aspects of string theory and supergravity

弦理论为研究量子理论如何改变时空几何提供了一个框架。最近，人们提倡将准厄米几何作为一种统一旧的“弦几何”的方法，比如双重几何和广义几何。该项目旨在系统地发展准厄米方法，并将其与其他现代全局方法结合起来研究时空和模空间的几何。它将考虑到其他最近的发展，例如包含可以在弦理论中通过对偶变换实现的奇异时空相。该项目的一个重点将是找出新的明确的例子，以澄清几何概念的推广在多大程度上导致新的和有趣的物理学。可能的案例研究包括：(i)在广义空间上通过降维得到的有效场论是怎样的？（ii）如果时空不是环面振动，使用双重几何有意义吗？（iii）某些场的动能为负或具有多个类时方向的奇异时空相是否可以通过任何物理过程与传统时空相联系，如果可以，对宇宙学（暗能量、暴胀）有何影响？（iv）黑洞热力学定律及其信息理论解释的含义是什么？

String theory provides a framework for investigating how quantum theory modifies the geometry of space-time. Very recently para-Hermitian geometry has been advocated as a way to unify older attempts at a genuine `string geometry', such as doubled geometry and generalized geometry. The project will aim to develop the para-Hermitian approach systematically and to combine it with other modern global approaches to the geometry of both space-time and moduli spaces. It will take into account other recent developments, such as the inclusion of exotic space-time phases which can be realized in string theory through duality transformations. One emphasis of the project will be to work out new explicit examples which allow to clarify to which extent proposed generalizations of geometrical concepts lead to new and interesting physics. Possible case studies include: (i) how do the effective field theories obtained by dimensional reduction on generalized spaces look like? (ii) does the use of doubled geometry makes sense if space-time is not a torus fibration? (iii) can exotic space-time phases where kinetic energy for some fields becomes negative, or which have multiple time-like directions be connected to conventional space-times by any physical process, and if yes, what are the implications for cosmology (dark energy, inflation)? (iv) what are the implications for the laws black hole thermodynamics and their information-theoretic interpretation?