Superconformal Flavor Simplified

TL;DR

This work tackles the flavor hierarchy problem by coupling Standard Model fields to a conformal sector and using a-maximization to determine exact $R$-charges, turning previously incalculable models into calculable ones. By focusing on simple vector-like SCFTs within an SU(5)$_{\mathrm{GUT}}$ framework, the authors quantify the constraints that perturbativity of the visible gauge couplings imposes on the conformal window and the need to minimize extra GUT-charged matter. A detailed scan across SU($N$) with adjoint, and Sp($2N$) with an antisymmetric tensor, including deformations by $\mathrm{Tr}[A^{k+1}]$, reveals that most minimal constructions hit the SU(5)$_{\mathrm{GUT}}$ Landau pole, but a narrow class, notably Sp(2N) with an antisymmetric and certain deformations, can satisfy the bound and generate the observed hierarchies. An analysis of an older, reportedly incalculable model shows it cannot realize a viable flavor pattern, illustrating the tight but navigable constraints. Overall, the paper demonstrates that calculable, high-scale conformal flavor models are possible but require carefully chosen, minimal CFT sectors to remain perturbative up to near the Planck or GUT scales, guiding future model-building efforts.

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.

Figures (1)

• Figure 1: Location of the $SU(5)_{\mathrm{GUT}}$ Landau pole as a function of the $\beta_{g_5}$-numerator $\mathcal{A}$, assuming that all new matter enters at $\Lambda_c \sim 10^{16} \, {\rm GeV}$.