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

我的研究重点是研究弦理论作为粒子物理和重力的基本理论。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。弦理论是一个建立良好且一致的框架。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课题。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果的关系。通常，纯数学和物理可以相互启发，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异质性/ f理论对偶性的核心，我们想在这个拨款提案中重点关注：在这种情况下，两种不同的弦理论在非常不同的几何上以互补的方式描述相同的物理。在这种情况下，两种理论都受益于其他技术可用的另一种理论中的不同公式。一般来说，当相互作用较小时，杂质弦在微扰状态下是很容易理解的。传统上，这一理论是标准模型之外许多现象学相关模型的良好起点。然而，关于所谓的非摄动结构以及它们的稳定化，即模稳定化的知识是非常有限的。另一方面，f理论提供了对非扰动方面的控制，并承诺统一其他弦理论的好处。近年来，f理论经历了一个快速发展的时期。特别是在f理论中对阿贝尔对称性的描述取得了重大的飞跃。这些对称性是描述诸如电磁力之类的力所必需的。然而，作为与现象学应用高度相关的G4通量的结构，其他成分仍然缺乏完整的描述。异质性/ f理论的二元性使我们能够将一种理论的见解映射到另一种理论，并用另一种理论补充一种理论中缺失的结构。然后，这些新的结构可以推广为有效的，甚至超越了对偶点。除了G4通量外，我们还想描绘两种理论中关于模稳定的成功发展。此外，f理论中对阿贝尔对称的控制将使我们能够构造新的异质对偶几何并揭示其未知的特征。最后，通过我们的探索，我们有了清晰的现象学应用：我们将把异质弦中的现象学吸引模型映射到f理论的对应物。在f理论中，我们将通过我们可以描述的非扰动效应来完成这些模型。有了这个提议，我们想把包括重力在内的粒子物理模型提升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.