Modular Flavour Symmetries and Modulus Stabilisation

Abstract

We study the problem of modulus stabilisation in the framework of the modular symmetry approach to the flavour problem. By analysing simple UV-motivated CP-invariant potentials for the modulus $\tau$ we find that a class of these potentials has (non-fine-tuned) CP-breaking minima in the vicinity of the point of ${\mathbb{Z}}_3^{ST}$ residual symmetry, $\tau \simeq e^{2\pi i/3}$. Stabilising the modulus at these novel minima breaks spontaneously the CP symmetry and can naturally explain the mass hierarchies of charged leptons and possibly of quarks.

27 pages, 4 figures, 1 table; comments and references added; matches version published in JHEP

References in corpus (4)

• Landscape of Modular Symmetric Flavor Models
• Eclectic flavor scheme from ten-dimensional string theory -- I. Basic results
• Spontaneous CP violation by modulus $\tau$ in $A_4$ model of lepton flavors
• Siegel modular flavor group and CP from string theory