# Unification of Flavor, CP, and Modular Symmetries

## TL;DR

This paper introduces a novel method using outer automorphisms of the Narain space group to unify flavor, CP, and modular symmetries in string theory, revealing geometry-dependent local flavor groups.

## Contribution

It develops a new approach to determine unified flavor symmetries in string theory, linking geometric properties to flavor structures and local symmetries.

## Key findings

- Unified flavor, CP, and modular symmetries depend on compact space geometry.
- Discovery of local flavor groups with different symmetries for various sectors.
- Potential connections to bottom-up flavor model building.

## Abstract

Flavor symmetry plays a crucial role in the standard model of particle physics but its origin is still unknown. We develop a new method (based on outer automorphisms of the Narain space group) to determine flavor symmetries within compactified string theory. A picture emerges where traditional (discrete) flavor symmetries, CP-like symmetries and modular symmetries (like T-duality) of string theory combine to unified flavor symmetries. The groups depend on the geometry of compact space and the geographical location of fields in the extra dimensions. We observe a phenomenon of "local flavor groups" with potentially different flavor symmetries for the various sectors of quarks and leptons. This should allow interesting connections to existing bottom-up attempts in flavor model building.