Eclectic flavor scheme from ten-dimensional string theory -- II. Detailed technical analysis

TL;DR

This paper analyzes the detailed structure of flavor symmetries arising from ten-dimensional string theory, focusing on modular and traditional symmetries, and how they combine into an eclectic flavor group influencing particle physics models.

Contribution

It provides a comprehensive top-down derivation of the eclectic flavor group from string theory, including modular, CP, and R-symmetries, and explores their implications for flavor structures.

Findings

Derived modular groups and symmetries for string compactifications

Identified how flavor symmetries depend on moduli space location

Provided a predictive framework for flavor symmetry in string theory

Abstract

String theory leads to a flavor scheme where modular symmetries play a crucial role. Together with the traditional flavor symmetries they combine to an eclectic flavor group, which we determine via outer automorphisms of the Narain space group. Unbroken flavor symmetries are subgroups of this eclectic group and their size depends on the location in moduli space. This mechanism of local flavor unification allows a different flavor structure for different sectors of the theory (such as quarks and leptons) and also explains the spontaneous breakdown of flavor- and CP-symmetries (via a motion in moduli space). We derive the modular groups, including CP and R-symmetries, for different sub-sectors of six-dimensional string compactifications and determine the general properties of the allowed flavor groups from this top-down perspective. It leads to a very predictive flavor scheme that should be confronted with the variety of existing bottom-up constructions of flavor symmetry in order to clarify which of them could have a consistent top-down completion.