Beyond Standard Modeling: Modular Symmetries and Non-Perturbative Methods
Abstract
In this thesis, we investigate the fundamental aspects of particle physics, specifically in the context of physics beyond the Standard Model. We focus on addressing two of the problems in this context: the flavor problem and the dynamical evolution of chiral symmetries.
We explore the flavor problem, specifically concerning the mystery behind the number of generations in the Standard Model (SM) by using the tools in supersymmetric theories to challenge notions of ‘generations’ as an invariant through RG flows from UV to IR. To achieve this, we perform a detailed analysis of non-perturbative field theoretic dynamics in supersymmetric models. This study not only offers profound insights into the peculiarities of QFTs but also helps navigate the string landscape of viable models. Furthermore, we also develop model-building tools to achieve mass gaps in chiral models, a crucial ingredient in generation flows, in full generality for various gauge groups.
In the second part of this thesis, we explore the flavor problem using the lens of modular symmetries. Focusing on a torus based approach, the underlying physical parameters in this methodology are derived by adding flux to the two compactified extra dimensions. In chapter 4, we wade through the strengths and challenges of this method. We can understand the flavor parameters by examining the modular-form Yukawas, and the overall symmetry group in terms of the flux parameters. Expanding on the strengths of the modular approach, in chapter 5, we also propose an eclectic scheme, where we draw from the union of modular and traditional discrete flavor groups in string theory, to provide a unified framework forunderstanding flavor physics.
Using mathematical analysis in various settings, be it stringy models, or supersymmetric theories, we present this thesis as a minor contribution to the search for an understanding of the puzzles of the Standard Model. It offers several model-building tools and frameworks that provide non-standard insights beyond the Standard Model.