Superconformal Flavor Simplified

TL;DR

This paper demonstrates that many supersymmetric flavor models, previously thought incalculable, are actually calculable using a-maximization, leading to simple viable models that explain flavor hierarchies.

Contribution

It shows how to apply a-maximization to construct and analyze simple vector-like flavor models within supersymmetry, addressing previous calculability issues.

Findings

Most models are calculable with a-maximization.

A small class of models can maintain perturbative gauge couplings.

Viable models can generate flavor hierarchies without losing calculability.

Abstract

A simple explanation of the flavor hierarchies can arise if matter fields interact with a conformal sector and different generations have different anomalous dimensions under the CFT. However, in the original study by Nelson and Strassler many supersymmetric models of this type were considered to be 'incalculable' because the R-charges were not sufficiently constrained by the superpotential. We point out that nearly all such models are calculable with the use of a-maximization. Utilizing this, we construct the simplest vector-like flavor models and discuss their viability. A significant constraint on these models comes from requiring that the visible gauge couplings remain perturbative throughout the conformal window needed to generate the hierarchies. However, we find that there is a small class of simple flavor models that can evade this bound.