Modular invariance and the QCD angle

Abstract

String compactifications on an orbi-folded torus with complex structure give rise to chiral fermions, spontaneously broken CP, modular invariance. We show that this allows simple effective theories of flavour and CP where: i) the QCD angle vanishes; ii) the CKM phase is large; iii) quark and lepton masses and mixings can be reproduced up to order one coefficients. We implement such general paradigm in supersymmetry or supergravity, with modular forms or functions, with or without heavy colored states.

arXiv comment32 pages, 2 figures, webinar presentation at https://www.youtube.com/watch?v=s0Vs5ykY36Y. Final version to appear on JHEP with extended discussion on the solution in supergravity

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• More about quark Yukawa textures from selection rules without group actions
• Finite modular axion and radiative moduli stabilization
• Neutrino Mass Sum Rules from Modular ${\mathcal{A}}_4$ Symmetry
• Non-holomorphic modular flavor symmetry and odd weight polyharmonic Maaß form
• Strong CP and Flavor in Multi-Higgs Theories
• Exploring the Landscape of Spontaneous CP Violation in Supersymmetric Theories
• Effective description of Nelson-Barr models and the theta parameter
• Natural solution of SUSY $\mu$ problem from modulus stabilization in modular flavor model
• Féeton ($B-L$ Gauge Boson) Dark Matter Testable in Future Direct Detection Experiments