Fermionic UV completions of Composite Higgs models

TL;DR

We address the problem of identifying UV completions for four-dimensional composite Higgs models built from purely fermionic matter. Our approach is strictly group-theoretical, imposing asymptotic freedom, anomaly constraints, custodial symmetry, and the existence of cubic hyper-color bound states that can act as top partners; we then classify viable hyper-color groups and fermion contents across $p=1,2,3$ irreps, yielding minimal cosets $SU(5)/SO(5)$ and $SU(4)/Sp(4)$ and, in a 2016 addendum, a coset $SU(4)\times SU(4)'/SU(4)_D$. The main contributions are a concrete catalog of models that could realize partial compositeness with purely fermionic UV completions, and a critical assessment of their viability given MAC dynamics, potential proton-decay issues, and Landau-pole concerns. This work clarifies the landscape of feasible UV completions and identifies the simplest and most promising constructions, while outlining key phenomenological caveats and directions for further refinement.

Abstract

We classify the four-dimensional purely fermionic gauge theories that give a UV completion of composite Higgs models. Our analysis is at the group theoretical level, addressing the necessary (but not sufficient) conditions for the viability of these models, such as the existence of top partners and custodial symmetry. The minimal cosets arising are those of type SU(5)/SO(5) and SU(4)/Sp(4). We list all the possible "hyper-color" groups allowed and point out the simplest and most promising ones.