Discrete flavor symmetries in D-brane models

TL;DR

This paper investigates how discrete flavor symmetries emerge in D-brane models of particle physics, analyzing their origins, types, and implications for Yukawa couplings in specific compactification scenarios.

Contribution

It provides a systematic method to identify and distinguish approximate and exact discrete flavor symmetries in D-brane models, including explicit examples with non-Abelian representations.

Findings

Discrete flavor symmetries can be explicitly constructed in D-brane models.

The flavor symmetry group can be D_4 or its tensor products in specific setups.

Explicit Pati-Salam models show non-Abelian family transformations affecting Yukawa couplings.

Abstract

We study the presence of discrete flavor symmetries in D-brane models of particle physics. By analyzing the compact extra dimensions of these models one can determine when such symmetries exist both in the context of intersecting and magnetized D-brane constructions. Our approach allows to distinguish between approximate and exact discrete symmetries, and it can be applied to compactification manifolds with continuous isometries or to manifolds that only contain discrete isometries, like Calabi-Yau three-folds. We analyze in detail the class of rigid D-branes models based on a Z_2 x Z'_2 toroidal orientifold, for which the flavor symmetry group is either the dihedral group D_4 or tensor products of it. We construct explicit Pati-Salam examples in which families transform in non-Abelian representations of the flavor symmetry group, constraining Yukawa couplings beyond the effect of massive U(1) D-brane symmetries.