Exploring the landscape of string theory flux vacua using exceptional field theory

弦理论，我们最发达的量子引力理论，只在十维中是一致的。尽管如此，我们可以通过“紧化”它来洞察低维物理，即考虑空间上的弦理论，其中一些维度构成了一个紧化空间。低维理论的许多性质，如粒子谱，都被编码在紧化空间的几何结构中。这使我们能够获得宇宙的弦理论预测。此外，“全息”将d维反德西特空间（一定的负弯曲空间）上的弦理论与D-1维中没有引力的量子场论联系起来。在过去的20年里，这导致了对量子场论的巨大的新见解，比如强核力或超导体的基础。在弦现象学和全息学中，考虑由“通量”穿透的紧化是很重要的，“通量”是电磁通量的高维推广。然而，我们缺乏对通量紧化的系统认识。因此，弦现象学只能研究可能紧化的一个子集，其中通量在几何上弱“反向反应”。此外，构造AdS真空的变形和研究AdS解的空间是困难的，这两者都包含了强耦合量子场论的重要信息，而这些信息往往不能直接研究。研究通量紧化的困难源于我们对黎曼几何的依赖。在这个项目中，我将使用最近制定的特殊场论，这是我大力帮助发展的。在这种形式中，通量和引力自由度是统一的，为研究通量紧化提供了一种完全自然的语言。此外，它还允许我们研究非几何弦背景，在这种背景下，我们通常的时空概念就失效了，无法使用传统工具进行分析。然而，这些非几何背景具有许多理想的现象学性质，并可能提供全息对偶性的新例子。本项目将系统地研究和分类弦理论中的超对称通量真空及其变形，并分析它们在现实的自然弦模型和全息中的作用。具体目标是：[A]分析一般四维超对称Minkowski真空的模空间和规范群。[B]了解超对称Minkowski通量真空的拓扑结构，并提出构造反反应通量真空的新方法。[C]对10维/11维超引力的所有超对称AdS真空进行分类，并搜索弦理论的非几何AdS真空。[D]构造超对称AdS真空的有限超对称和超对称破缺变形。[E]研制全息词典，用于全息术的精度测试。

String theory, our most-developed theory of quantum gravity, is only consistent in ten dimensions. Nonetheless, we can obtain insight into lower-dimensional physics by "compactifying" it, i.e. considering string theory on spaces where some dimensions make up a compact space. Many properties of the lower-dimensional theories, such as the spectrum of particles, are encoded in the geometry of the compact space. This allows us to obtain string theory predictions for our universe.Moreover, "holography" relates string theory on D-dimensional Anti-de Sitter space, a certain negatively-curved space, times a compact space to quantum field theories without gravity in D-1 dimensions. Over the last 20 years, this has led to tremendous new insight into quantum field theories such as those underlying the strong nuclear force or superconductors.In both string phenomenology and holography, it is important to consider compactifications pierced by "fluxes", higher-dimensional generalisations of electromagnetic flux. Yet, we are lacking a systematic understanding of flux compactifications. As a result, string phenomenology has only been able to study a subset of possible compactifications, where the fluxes weakly "backreact" on the geometry. Moreover, it is difficult to construct deformations of AdS vacua and to study the space of AdS solutions, both of which contain important information about strongly-coupled quantum field theories which can often not be studied directly.The difficulty in studying flux compactifications stems from our reliance on Riemanniangeometry. In this project, I will instead use the recently-formulated Exceptional Field Theory, which I have substantially helped develop. In this formalism, fluxes and gravitational degrees of freedom are unified, providing an entirely natural language in which to study flux compactifications. Moreover, it allows us to study non-geometric string backgrounds, on which our usual notions of spacetime break down and which cannot be analysed using conventions tools. Yet, these non-geometric backgrounds have many desirable phenomenological properties and may provide new examples of holographic dualities.This project will systematically investigate and classify the supersymmetric flux vacua of string theory and their deformations, and analyse their role in realistic string-models of nature and holography. The specific goals are to:[A] Analyse the moduli space and gauge groups of generic 4-dimensional supersymmetric Minkowski vacua.[B] Understand the topology of supersymmetric Minkowski flux vacua and develop new methods of constructing backreacted flux vacua.[C] Classify all supersymmetric AdS vacua of 10-/11-dimensional supergravity, and search for non-geometric AdS vacua of string theory.[D] Construct finite supersymmetric and supersymmetry-breaking deformations of supersymmetric AdS vacua.[E] Develop a holographic dictionary that is useful for precision tests of holography.