Yukawa hierarchies in global F-theory models

• Published in: The journal of high energy physics Vol. 2020; no. 1; pp. 1 - 27
• Main Authors: Cvetič, Mirjam, Lin, Ling, Liu, Muyang, Zhang, Hao Y., Zoccarato, Gianluca
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2020; Springer Nature B.V; Springer Berlin; SpringerOpen
• Subjects: Classical and Quantum Gravitation; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Couplings; Elementary Particles; F-Theory; Hierarchies; High energy physics; Instantons; Mathematical analysis; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Supersymmetric Effective Theories; Supersymmetric Effective Theories; F-Theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP01(2020)037

A bstract We argue that global F-theory compactifications to four dimensions gener- ally exhibit higher rank Yukawa matrices from multiple geometric contributions known as Yukawa points. The holomorphic couplings furthermore have large hierarchies for generic complex structure moduli. Unlike local considerations, the compact setup realizes these features all through geometry, and requires no instanton corrections. As an example, we consider a concrete toy model with SU(5) × U(1) gauge symmetry. From the geometry, we find two Yukawa points for the 1 0 − 2 5 ¯ 6 5 ¯ − 4 coupling, producing a rank two Yukawa matrix. Our methods allow us to track all complex structure dependencies of the holomorphic couplings and study the ratio numerically. This reveals hierarchies of O (10 5 ) and larger on a full-dimensional subspace of the moduli space.