Classification of discrete modular symmetries in Type IIB flux vacua

Abstract

We classify discrete modular symmetries in the effective action of Type IIB string on toroidal orientifolds with three-form fluxes, emphasizing on $T^6/{\mathbb{Z}}_2$ and $T^6/({\mathbb{Z}}_2\times {\mathbb{Z}}_2^{\prime })$ orientifold backgrounds. On the three-form flux background, the modular group is spontaneously broken down to its congruence subgroup whose pattern is severely constrained by a quantization of fluxes and tadpole cancellation conditions. We explicitly demonstrate that the congruence subgroups appearing in the effective action arise on magnetized D-branes wrapping certain cycles of tori.

22 pages, v2: published version, typos corrected

References in corpus (17)

• On the Geometry of the String Landscape and the Swampland
• Monodromy in the CMB: Gravity Waves and String Inflation
• The Swampland: Introduction and Review
• Unification of Flavor, CP, and Modular Symmetries
• Modular $S_4$ and $A_4$ Symmetries and Their Fixed Points: New Predictive Examples of Lepton Mixing
• A modular $A_4$ symmetry realization of two-zero textures of the Majorana neutrino mass matrix
• Eclectic Flavor Groups
• Modular symmetry origin of texture zeros and quark lepton unification
• Type II seesaw models with modular $A_4$ symmetry
• Lepton Flavor Mixing and CP Violation in the Minimal Type-(I+II) Seesaw Model with a Modular $A_4$ Symmetry
• $CP$ violation in modular invariant flavor models
• Higher Order Couplings in Magnetized Brane Models
• Zero-modes on orbifolds : magnetized orbifold models by modular transformation
• Higher Order Couplings from Heterotic Orbifold Theory
• An Inverse Seesaw model with $A_4$-modular symmetry
• Non-Abelian discrete flavor symmetries of 10D SYM theory with magnetized extra dimensions
• F-theory Flux Vacua and Attractor Equations

Cited by in corpus (25)

• Double Cover of Modular $S_4$ for Flavour Model Building
• Revisiting modular symmetry in magnetized torus and orbifold compactifications
• Fermion Mass Hierarchies, Large Lepton Mixing and Residual Modular Symmetries
• Landscape of Modular Symmetric Flavor Models
• Double Covering of the Modular $A_5^{}$ Group and Lepton Flavor Mixing in the Minimal Seesaw Model
• Automorphic Forms and Fermion Masses
• Modular flavor symmetries of three-generation modes on magnetized toroidal orbifolds
• Spontaneous CP violation and symplectic modular symmetry in Calabi-Yau compactifications
• CP Symmetry and Symplectic Modular Invariance
• Challenge for spontaneous CP violation in Type IIB orientifolds with fluxes
• Dirac neutrino mass models with a modular $S_4^{}$ symmetry
• Symplectic modular symmetry in heterotic string vacua: flavor, CP, and $R$-symmetries
• Residual flavor symmetry breaking in the landscape of modular flavor models
• $A_4$ Modular Flavour Model of Quark Mass Hierarchies close to the Fixed Point $\tau =\omega$
• Modular symmetry in the SMEFT
• A minimal modular invariant neutrino model
• Top-Down Anatomy of Flavor Symmetry Breakdown
• Modular flavor symmetry and vector-valued modular forms
• 4D modular flavor symmetric models inspired by higher dimensional theory
• Lepton mass matrix from double covering of $A_4$ modular flavor symmetry
• Common origin of the strong CP and CKM phases in string compactifications
• Modular Invariant Models of Leptons at Level 7
• Flavor, CP and Metaplectic Modular Symmetries in Type IIB Chiral Flux Vacua
• Natural solution of SUSY $\mu$ problem from modulus stabilization in modular flavor model
• Modular Flavour Symmetries and Modulus Stabilisation