D-branes at Toric Singularities: Model Building, Yukawa Couplings and Flavour Physics

TL;DR

This paper explores D-brane model building at toric singularities, revealing constraints on family numbers, mass hierarchies, and realistic flavor mixing, with implications for string phenomenology.

Contribution

It demonstrates that toric phases typically have at most three families, and shows how realistic Yukawa couplings and CP violation can emerge from these models.

Findings

Number of families ≤ 3 in toric phases, except for one case.

Mass hierarchies among quarks can be achieved with massless lightest family.

Explicit CKM matrices show realistic flavor mixing and CP violation.

Abstract

We discuss general properties of D-brane model building at toric singularities. Using dimer techniques to obtain the gauge theory from the structure of the singularity, we extract results on the matter sector and superpotential of the corresponding gauge theory. We show that the number of families in toric phases is always less than or equal to three, with a unique exception being the zeroth Hirzebruch surface. With the physical input of three generations we find that the lightest family of quarks is massless and the masses of the other two can be hierarchically separated. We compute the CKM matrix for explicit models in this setting and find the singularities possess sufficient structure to allow for realistic mixing between generations and CP violation.