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

使用例外场理论探索弦理论通量真空景观

• 批准号: 426510644
• 负责人: Dr. Emanuel Malek
• 金额: --
• 依托单位: Institut für Physik
• 依托单位国家: 德国
• 项目类别: Independent Junior Research Groups
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/426510644?language=en
• 关键词: Exploring; landscape; string; theory; flux

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.

弦理论，我们最发达的量子引力理论，只在10维中是一致的。尽管如此，我们可以通过“紧致化”来深入了解低维物理，也就是说，考虑一些维构成紧致空间的空间上的弦理论。低维理论的许多性质，如粒子谱，都被编码在紧致空间的几何中。这使我们能够得到弦理论对我们宇宙的预言，而且，“全息术”把D维反德西特空间（一个负弯曲的空间，乘以一个紧致空间）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，例如强核力或超导体的基础。在弦现象学和全息学中，考虑被“通量”穿透的紧化是很重要的，“通量”是电磁通量的高维概括。然而，我们对通量紧致化缺乏系统的理解。因此，弦唯象学只能研究可能的紧化的一个子集，其中通量对几何的“反作用”很弱。此外，构造AdS真空的形变和研究AdS解的空间都是困难的，这两个问题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。通量紧化研究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例外场理论，我在很大程度上帮助发展。在这种形式主义中，通量和引力自由度是统一的，提供了一个完全自然的语言来研究通量紧化。此外，它使我们能够研究非几何弦背景，在这种背景上，我们通常的时空概念被打破，而且不能用常规工具进行分析。然而，这些非几何背景有许多令人满意的唯象性质，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的超对称通量真空及其变形，并分析它们在自然和全息的现实弦模型中的作用。具体目标是：[A]分析一般四维超对称闵可夫斯基真空的模空间和规范群。[B]理解超对称闵可夫斯基通量真空的拓扑结构，并发展新的构造反作用通量真空的方法。[C]对10-/11维超引力的超对称AdS真空进行分类，并寻找弦理论的非几何AdS真空。[D]构造超对称AdS真空的有限超对称形变和超对称破缺形变。[E]开发一个全息字典，对全息术的精确测试有用。