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

TL;DR

This paper explores the unification of modular, traditional flavor, CP, and R-symmetries within string theory's six-dimensional compactifications, revealing their common origin and implications for flavor model building.

Contribution

It extends the eclectic flavor symmetry framework from two to six extra dimensions in string theory, uncovering new insights into CP breaking and R-symmetries as remnants of modular symmetries.

Findings

Unified origin of all symmetries in string theory

New interpretation of R-symmetries as remnants of modular symmetries

High predictive power of the eclectic flavor scheme

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.