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，仿厄米几何被提倡作为一种方法，以统一旧的尝试在一个真正的“弦几何”，如加倍几何和广义几何。该项目的目标是系统地发展准厄米方法，并将其与时空和模空间几何学的其他现代全球方法联合收割机结合起来。它将考虑到其他最近的发展，如包括奇异的时空相位，可以实现在弦理论通过对偶变换。该项目的一个重点将是制定新的明确的例子，允许澄清在何种程度上提出的几何概念的概括导致新的和有趣的物理。可能的案例研究包括：（i）如何有效的场论得到的降维广义空间看起来像？(ii)如果时空不是环面纤维化，那么使用双重几何有意义吗？(iii)某些场的动能变为负值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常规时空相联系，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?