The heterotic/F-theory duality: Fluxes and models of particle physics

我的研究重点是弦理论作为粒子物理学和引力的基础理论的调查。这个迷人的理论提供了一种将物理学重新表述为几何性质的方法。弦理论是一个完善的、一致的框架。然而，它还没有被完全理解，并且是数学和物理界面上正在进行的研究的主题。在过去的几十年里，物理学和数学之间的这种联系是一种非常富有成效的关系。通常，纯数学和物理学可以相互启发，因为它们以互补的方式描述相同的过程。一个非常相似的关系也存在于杂化/F-理论对偶的核心，这是我们在这个资助申请中要关注的：在这种情况下，两个不同几何的弦理论以互补的方式描述了同一物理。在这种情况下，两种理论都受益于另一种理论的不同表述，而另一种理论则有其他技术可用。一般来说，杂合弦在微扰区域中，当相互作用是小尺度的时候，是很好理解的。传统上，这一理论是一个很好的起点，许多现象学相关的模型超出了标准模型。然而，所谓的非微扰结构以及它们的稳定化，称为模稳定化的知识是非常有限的。另一方面，F理论提供了对非微扰方面的控制，并有望统一其他弦理论的优点。近年来，F理论经历了一个快速发展的时期。特别是在F-理论的阿贝尔对称性的描述作出了重大的飞跃。这些对称性是描述电磁力等力所必需的。然而，其他成分仍然缺乏一个完整的描述，作为建设的G4通量是高度相关的现象学应用。杂种优势/F理论的对偶性使我们能够将一种理论的见解映射到另一种理论，并通过另一种理论补充一种理论中缺失的结构。这些新的结构然后可以被推广为有效的，甚至超越了点的对偶性。除了G4通量，我们还希望映射两种理论中关于模量稳定的成功发展。此外，在F-理论中对阿贝尔对称的控制将使我们能够构造新的杂化对偶几何，并揭示其未知的特征。最后，通过我们的探索，我们有明确的现象学应用：我们将映射的现象学吸引力的模型在杂化弦的F-理论对应。在F理论中，我们将通过我们可以在那里描述的非微扰效应来完成这些模型。有了这个提议，我们希望把粒子物理学模型，包括引力，带到一个新的复杂水平。

My research focuses on the investigation of string theory as a fundamental theory of particle physics and gravity. This fascinating theory provides a way to reformulate physics into geometric properties. String theory is a well established and consistent framework. However it is not yet fully understood and a topic of ongoing research at the interface of mathematics and physics. Over the last decades this connection between physics and mathematics has been a very fruitful relationship. Oftentimes pure mathematics and physics could inspire each other as they describe the same processes in complementary ways. A very similar relationship also lies at the heart of the Heterotic/F-theory duality which we want to focus on in this grant proposal: In this case two different string theories on very different geometries describe the same physics in complementary ways. In such cases both theories benefit from a different formulation in the other theory where other techniques are available. In general the heterotic string is very well understood in the perturbative regime when the interactions are of small size. Traditionally this theory is a good starting point for many phenomenologically relevant models beyond the standard model. However the knowledge of so called non-perturbative structures as well as their stabilization, called moduli stabilization is very limited. F-theory on the other hand offers control over non-perturbative aspects and promises to unify benefits from other string theories. F-theory experienced a period of rapid development in the recent years. In particular the description of Abelian symmetries in F-theory made a major leap forward. These symmetries are needed to describe forces such as electromagnetism. However, other ingredients still lack a complete description as the construction of G4 fluxes that are of high relevance for phenomenological applications. The Heterotic/F-theory duality enables us to map insights from one theory to the other and complement missing structures in one theory by the other. These new structures can then be generalized to be valid even beyond the point of the duality. Apart from G4 flux we also want to map the successful developments concerning moduli stabilization in both theories. Moreover the control over Abelian symmetries in F-theory will enable us to construct new heterotic dual geometries and uncover their yet unknown features. Finally with our explorations we have clear phenomenological applications in mind: We will map the phenomenological appealing models in the heterotic string to F-theory counterparts. Within F-theory we will complete those models by non-perturbative effects that we can describe there. With this proposal we want to bring models of particle physics including gravity to a new level of sophistication.