Eclectic flavor scheme from ten-dimensional string theory – I. Basic results

Hans Peter Nilles,Saúl Ramos–Sánchez,Patrick K.S Vaudrevange

doi:10.1016/j.physletb.2020.135615

Abstract

In a consistent top-down approach based on orbifold compactifications, modular and traditional flavor symmetries combine nontrivially to the so-called eclectic flavor symmetry. We extend this scheme from two extra dimensions, discussed previously, to the six extra dimensions of string theory. By doing so, new insights on the nature of CP and its spontaneous breaking emerge. Moreover, we identify a new interpretation of R-symmetries as unbroken remnants from modular symmetries that are associated with geometrically stabilized complex structure moduli. Hence, all symmetries (i.e. modular, traditional flavor, CP and R) share a common origin in string theory: on a technical level, they are given by outer automorphisms of the Narain space group. The eclectic top-down approach leads to a very restrictive scheme with high predictive power. It remains a challenge to connect this with existing bottom-up constructions of modular flavor symmetry.

Highlights

We present a study of the eclectic flavor approach [1,2] from the point of view of ten-dimensional (10d) string theory with six compact dimensions
New information is especially relevant in view of CP and, R-symmetries that appear as remnants of the Lorentz group in six extra dimensions
The bilinear Kahler potential (which is essentially unconstrained in bottom-up models based solely on modular symmetries [27]) is very sensitive to the eclectic extension: starting with only T, the Kahler potential of localized strings contains non-diagonal terms, which are removed by the traditional flavor symmetry ∆(54) to all orders in the Kahler modulus T

Summary

Introduction

We present a study of the eclectic flavor approach [1,2] from the point of view of ten-dimensional (10d) string theory with six compact dimensions. The full picture leads to an enlargement of the eclectic flavor group as well as its subgroups that represent enhanced local flavor symmetries at specific points (or other sub-loci) in moduli space. These enhanced symmetries appear due to the alignment of vacuum expectation values (vevs) of so-called moduli fields and might include CP-like symmetries. These are mainly due to remnant symmetries of the modular group of the complex structure moduli and they enhance the eclectic flavor symmetry by R-symmetries.

Status of flavor symmetries in string orbifolds

New insights from six compact dimensions

Flavor R-symmetries from modular symmetries

Local flavor unification with modular R-symmetries

Conclusions and outlook