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

点击翻译按钮获取中文摘要

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.