Automorphic forms and fermion masses

• Published in: The journal of high energy physics Vol. 2021; no. 1; pp. 1 - 60
• Main Authors: Ding, Gui-Jun, Feruglio, Ferruccio, Liu, Xiang-Gan
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 08.01.2021; Springer Nature B.V; SpringerOpen
• Subjects: Analytic functions; Classical and Quantum Gravitation; Couplings; Discrete Symmetries; Elementary Particles; Fermions; High energy physics; Leptons; Lie groups; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Quark Masses and SM Parameters; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Subgroups; Supersymmetric Effective Theories; Supersymmetry; Discrete Symmetries; Supersymmetric Effective Theories; Quark Masses and SM Parameters
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP01(2021)037

A bstract We extend the framework of modular invariant supersymmetric theories to encompass invariance under more general discrete groups Γ, that allow the presence of several moduli and make connection with the theory of automorphic forms. Moduli span a coset space G / K , where G is a Lie group and K is a compact subgroup of G , modded out by Γ. For a general choice of G , K , Γ and a generic matter content, we explicitly construct a minimal Kähler potential and a general superpotential, for both rigid and local N = 1 supersymmetric theories. We also specialize our construction to the case G = Sp(2 g, ℝ), K = U( g ) and Γ = Sp(2 g, ℤ), whose automorphic forms are Siegel modular forms. We show how our general theory can be consistently restricted to multi-dimensional regions of the moduli space enjoying residual symmetries. After choosing g = 2, we present several examples of models for lepton and quark masses where Yukawa couplings are Siegel modular forms of level 2.