Siegel modular flavor group and CP from string theory

Abstract

We derive the potential modular symmetries of heterotic string theory. For a toroidal compactification with Wilson line modulus, we obtain the Siegel modular group $\mathrm{Sp}(4,\mathbb{Z})$ that includes the modular symmetries $\mathrm{SL}(2,\mathbb{Z}{)}_T$ and $\mathrm{SL}(2,\mathbb{Z}{)}_U$ (of the "geometric" moduli $T$ and $U$) as well as mirror symmetry. In addition, string theory provides a candidate for a CP-like symmetry that enhances the Siegel modular group to $\mathrm{GSp}(4,\mathbb{Z})$.

arXiv comment18 pages, 1 figure, 1 table; v2: some statements in the conclusions clarified, matches version published in PLB

References in corpus (17)

• Unification of Flavor, CP, and Modular Symmetries
• CP Violation from Finite Groups
• A String Theory of Flavor and CP
• Multiple modular symmetries as the origin of flavour
• Lessons from eclectic flavor symmetries
• Moduli Dependence of One--Loop Gauge Couplings in (0,2) Compactifications
• Eclectic flavor scheme from ten-dimensional string theory -- II. Detailed technical analysis
• Moduli Spaces and Target Space Duality Symmetries in $(0,2)Z_N$ Orbifold Theories with Continuous Wilson Lines
• CP violation and modular symmetries
• K3 surfaces, modular forms, and non-geometric heterotic compactifications
• The eclectic flavor symmetry of the ${\mathbb{Z}}_2$ orbifold
• Spontaneous CP violation and symplectic modular symmetry in Calabi-Yau compactifications
• Geometric scaling in high-energy QCD at nonzero momentum transfer
• Geometry of Rank Reduction
• T-duality orbifolds of heterotic Narain compactifications
• The effect of Wilson line moduli on CP-violation by soft supersymmetry breaking terms
• A Worldsheet Perspective on Heterotic T-Duality Orbifolds

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• 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 $\tau =\omega$
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• Top-Down Anatomy of Flavor Symmetry Breakdown
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• 4D modular flavor symmetric models inspired by higher dimensional theory
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• Completing the eclectic flavor scheme of the ${\mathbb{Z}}_2$ orbifold
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• Modular flavored dark matter
• Modular Flavour Symmetries and Modulus Stabilisation
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