Solving Flavor Puzzles with Quiver Gauge Theories

TL;DR

This work embeds the Froggatt–Nielsen flavor mechanism into D-brane–derived quiver gauge theories with anomalous U(1) symmetries, leveraging Green–Schwarz anomaly cancellation to fix FN charges and enable a highly predictive flavor structure. In particular, SU(5) GUT realizations require an extended $U(5)\times U(5)$ quiver; the FN field S sits in a bifundamental and defines a suppression parameter $\epsilon$ via $\epsilon \equiv \langle S\rangle / M_V$, with the FN symmetry identified as $U(1)_{\rm L-R}$. The stringent charge constraints lead to a unique viable pattern for the up/down sectors and, crucially, predict neutrino mass anarchy in the lepton sector (quasi- or full-anarchy depending on charged assignments). Nonperturbative or spontaneous breaking of $U(1)_{\rm L+R}$ to $\mathbb{Z}_5$ can generate needed up-type masses without spoiling the overall structure, preserving the anarchy prediction. Overall, the approach sharpens the FN mechanism’s predictive power by tying flavor hierarchies to the geometry and anomaly structure of string-inspired quivers, with concrete SU(5) phenomenology linking quark hierarchies to anarchical neutrino masses.

Abstract

We consider a large class of models where the SU(5) gauge symmetry and a Froggatt-Nielsen (FN) Abelian flavor symmetry arise from a U(5)\times U(5) quiver gauge theory. An intriguing feature of these models is a relation between the gauge representation and the horizontal charge, leading to a restricted set of possible FN charges. Requiring that quark masses are hierarchical, the lepton flavor structure is uniquely determined. In particular, neutrino mass anarchy is predicted.

Figures (10)

• Figure 1: A D-brane construction with an $SU(5)$ gauge group and a distinct $U(1)_{\rm FN}$. The fundamental fields are strings stretching between the two stacks and are thus charged under the FN group, while the antisymmetric fields connect only to the $U(5)$ stack and have no $U(1)_{\rm FN}$ charge.
• Figure 2: Successive Higgsing of the $Y^{3,0}$ quiver diagram to a $\mathbb{C}^3$ quiver: a) The $Y^{3,0}$ quiver diagram; b) The effective quiver diagram induced by Higgsing $Z^1\propto\bf1$; c) The $\mathbb{C}^3/\mathbb{Z}_3$ quiver induced by Higgsing also $Z^2,Z^3\propto\bf1$.
• Figure 3: Breaking the $Y^{3,0}$ quiver by a diagonal VEV with two different eigenvalues with multiplicities $n$ and $N-n$.
• Figure 4: Diagrams for generating interactions suppressed by different factors $<S>/M_V$ using only cubic interactions.
• Figure 5: A directed quiver diagram for an $\epsilon^3$-suppression of the effective $\Phi_1\Phi_2\Phi_3$ term in the superpotential.