Automorphic Forms and Fermion Masses

Abstract

We extend the framework of modular invariant supersymmetric theories to encompass invariance under more general discrete groups $\Gamma$, 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 $\Gamma$. For a general choice of $G$, $K$, $\Gamma$ 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 $G=Sp(2g,R)$, $K=U(g)$ and $\Gamma =Sp(2g,Z)$, 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.

arXiv comment60 pages, 1 figure

References in corpus (54)

• The fate of hints: updated global analysis of three-flavor neutrino oscillations
• Discrete Flavor Symmetries and Models of Neutrino Mixing
• Target Space Duality in String Theory
• Four-dimensional String Compactifications with D-Branes, Orientifolds and Fluxes
• Toward Realistic Intersecting D-Brane Models
• Noncompact Symmetries in String Theory
• Effects of D-instantons
• Computing Yukawa Couplings from Magnetized Extra Dimensions
• Yukawa couplings in intersecting D-brane models
• Supersymmetry Constraints on Type IIB Supergravity
• Neutrino mixing from finite modular groups
• On $R^4$ threshold corrections in IIB string theory and (p,q) string instantons
• Running quark and lepton parameters at various scales
• Unification of Flavor, CP, and Modular Symmetries
• Trimaximal Neutrino Mixing from Modular A4 Invariance with Residual Symmetries
• Modular Invariance Faces Precision Neutrino Data
• Progress in D-brane model building
• Generalised CP Symmetry in Modular-Invariant Models of Flavour
• Neutrino Masses and Mixing from Double Covering of Finite Modular Groups
• Modular $S_4$ and $A_4$ Symmetries and Their Fixed Points: New Predictive Examples of Lepton Mixing
• Non-Abelian Discrete Flavor Symmetries from Magnetized/Intersecting Brane Models
• A String Theory of Flavor and CP
• A note on the predictions of models with modular flavor symmetries
• Soft scalar masses in supergravity with horizontal U(1)_X gauge symmetry
• Multiple modular symmetries as the origin of flavour
• Automorphic properties of low energy string amplitudes in various dimensions
• (0,2) Heterotic Gauge Couplings and their M-Theory Origin
• Eclectic Flavor Groups
• Lessons from eclectic flavor symmetries
• Revisiting modular symmetry in magnetized torus and orbifold compactifications
• Complete structure of Z_n Yukawa couplings
• Moduli Dependence of One--Loop Gauge Couplings in (0,2) Compactifications
• Modular symmetry by orbifolding magnetized $T^2\times T^2$: realization of double cover of ${\Gamma }_N$
• Higher Twisted Sector Couplings of $Z_N$ Orbifolds
• Periods and Duality Symmetries in Calabi-Yau Compactifications
• Eclectic flavor scheme from ten-dimensional string theory -- I. Basic results
• A note on non-perturbative R^4 couplings
• Realistic Yukawa Couplings through Instantons in Intersecting Brane Worlds
• Eisenstein series and automorphic representations
• Half-integral weight modular forms and application to neutrino mass models
• CP violation and modular symmetries
• Fermion Wavefunctions in Magnetized branes: Theta identities and Yukawa couplings
• Classification of discrete modular symmetries in Type IIB flux vacua
• Yukawa Couplings for Bosonic $Z_N$ Orbifolds: Their Moduli and Twisted Sector Dependence
• Heterotic Yukawa couplings and continuous Wilson lines
• Modular symmetry in magnetized/intersecting D-brane models
• The CKM Phase in Heterotic Orbifold Models
• Modular Weights, U(1)'s and Mass Matrices
• Dynamical mass matrices from effective superstring theories
• Two loop superstring amplitudes and S_6 representations
• Moduli and Twisted Sector Dependence of Z_N x Z_M Orbifold Couplings
• Flavor changing neutral current constraints on standard-like orbifold models
• On the modular invariance of mass eigenstates and CP violation
• A tour on Hermitian symmetric manifolds

Cited by in corpus (33)

• Modular Invariant Dynamics and Fermion Mass Hierarchies around $\tau =i$
• Fermion Mass Hierarchies, Large Lepton Mixing and Residual Modular Symmetries
• Double Covering of the Modular $A_5^{}$ Group and Lepton Flavor Mixing in the Minimal Seesaw Model
• Metaplectic Flavor Symmetries from Magnetized Tori
• Fermion Masses and Mixing from Double Cover and Metaplectic Cover of $A_5$ Modular Group
• Modular Invariant $A_4$ Models for Quarks and Leptons with Generalized CP Symmetry
• $SU(5)$ GUTs with $A_4$ modular symmetry
• CP Symmetry and Symplectic Modular Invariance
• Symplectic modular symmetry in heterotic string vacua: flavor, CP, and $R$-symmetries
• The first string-derived eclectic flavor model with realistic phenomenology
• Modular $S_4\times SU(5)$ GUT
• $A_4$ Modular Flavour Model of Quark Mass Hierarchies close to the Fixed Point $\tau =\omega$
• Modular symmetry at level 6 and a new route towards finite modular groups
• The symmetry approach to quark and lepton masses and mixing
• A minimal modular invariant neutrino model
• Fermion masses, critical behavior and universality
• Modulus $\tau$ linking leptonic CP violation to baryon asymmetry in $A_4$ modular invariant flavor model
• Top-Down Anatomy of Flavor Symmetry Breakdown
• Flipped SU(5) with modular $A_4$ symmetry
• Leptogenesis in $SO(10)$ Models with $A_4$ Modular Symmetry
• Flavor mixing and CP violation from the interplay of $S_4$ modular group and gCP
• Subcritical regime of hybrid inflation with modular $A_4$ symmetry
• Electron EDM arising from modulus $\tau$ in the supersymmetric modular invariant flavor models
• Modular flavor symmetry and vector-valued modular forms
• 4D modular flavor symmetric models inspired by higher dimensional theory
• Nonholomorphic $A_4$ modular invariance for fermion masses and mixing in SU(5) GUT
• Zero-modes in magnetized $T^6/{\mathbb{Z}}_N$ orbifold models through $Sp(6,\mathbb{Z})$ modular symmetry
• Completing the eclectic flavor scheme of the ${\mathbb{Z}}_2$ orbifold
• Quark-lepton mass relations from modular flavor symmetry
• FCNCs, Proton Stability, $g_{\mu }-2$ Discrepancy, Neutralino cold Dark Matter in Flipped $SU(5)\times U(1{)}_{\chi }$ from $F$ Theory with $A_4$ Symmetry
• $SO(10)$ models with $A_4$ modular symmetry
• Modular flavored dark matter
• Modular Flavour Symmetries and Modulus Stabilisation