Spontaneous CP violation and symplectic modular symmetry in Calabi-Yau compactifications

Abstract

We explore the geometrical origin of CP and the spontaneous CP violation in Calabi-Yau compactifications. We find that the CP symmetry is identified with an outer automorphism of the symplectic modular group in the large complex structure regime of Calabi-Yau threefolds, thereby enlarging the symplectic modular group to their semidirect product group. The spontaneous CP violation is realized by the introduction of fluxes, whose effective action is invariant under CP as well as the discrete ${\mathbb{Z}}_2$ symmetry or ${\mathbb{Z}}_4$ R-symmetry. We explicitly demonstrate the spontaneous CP violation on a specific Calabi-Yau threefold.

arXiv comment23 pages, v2:published version

References in corpus (29)

• CFT's From Calabi-Yau Four-folds
• Four-dimensional String Compactifications with D-Branes, Orientifolds and Fluxes
• The effective action of N=1 Calabi-Yau orientifolds
• Mirror Symmetry for Two Parameter Models -- II
• The effective action of Type IIA Calabi-Yau orientifolds
• Lepton Masses and Mixing from Modular $S_4$ Symmetry
• Neutrino mixing from finite modular groups
• Unification of Flavor, CP, and Modular Symmetries
• Trimaximal Neutrino Mixing from Modular A4 Invariance with Residual Symmetries
• Modular Invariance Faces Precision Neutrino Data
• Modular $A_4$ invariance and neutrino mixing
• CP violation of quarks in $A_4$ modular invariance
• CP Violation from Finite Groups
• Finite modular subgroups for fermion mass matrices and baryon/lepton number violation
• Automorphisms in Gauge Theories and the Definition of CP and P
• $SU(5)$ Grand Unified Theory with $A_4$ Modular Symmetry
• Modular symmetry and non-Abelian discrete flavor symmetries in string compactification
• Of CP and other Gauge Symmetries in String Theory
• Is CP a Gauge Symmetry?
• Revisiting modular symmetry in magnetized torus and orbifold compactifications
• $CP$ violation in modular invariant flavor models
• Periods for Calabi--Yau and Landau--Ginzburg Vacua
• CP violation and modular symmetries
• Classification of discrete modular symmetries in Type IIB flux vacua
• Challenge for spontaneous CP violation in Type IIB orientifolds with fluxes
• CP Violation and Moduli Stabilization in Heterotic Models
• $\mathcal{C}\mathcal{P}$ Violation from String Theory
• CP in Orbifold Models
• CP Violation and Dilaton Stabilization in Heterotic String Models

Cited by in corpus (25)

• Landscape of Modular Symmetric Flavor Models
• Eclectic flavor scheme from ten-dimensional string theory -- II. Detailed technical analysis
• Siegel modular flavor group and CP from string theory
• 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
• The symmetry approach to quark and lepton masses and mixing
• Fermion masses, critical behavior and universality
• Top-Down Anatomy of Flavor Symmetry Breakdown
• Moduli inflation from modular flavor symmetries
• Leptogenesis in $SO(10)$ Models with $A_4$ Modular Symmetry
• Sharpening the Boundaries Between Flux Landscape and Swampland by Tadpole Charge
• Time reversal and $\mathbf{CP}$ invariance in Calabi-Yau compactifications
• Lepton mass matrix from double covering of $A_4$ modular flavor symmetry
• 4D modular flavor symmetric models inspired by higher dimensional theory
• Classifications of magnetized $T^4$ and $T^4/Z_2$ orbifold models
• Remark on modular weights in low-energy effective field theory from type II string theory
• Modular symmetry anomaly and non-perturbative neutrino mass terms in magnetized orbifold models
• Flavor, CP and Metaplectic Modular Symmetries in Type IIB Chiral Flux Vacua
• Zero-modes in magnetized $T^6/{\mathbb{Z}}_N$ orbifold models through $Sp(6,\mathbb{Z})$ modular symmetry
• Generalized Matter Parities from Finite Modular Symmetries
• CP-like Symmetry with Discrete and Continuous Groups and CP Violation/Restoration
• Natural solution of SUSY $\mu$ problem from modulus stabilization in modular flavor model
• Modular Flavour Symmetries and Modulus Stabilisation