Holographic models of composite Higgs in the Veneziano limit. Part II. Fermionic sector

TL;DR

This paper extends holographic models to include fermionic sectors in strongly-coupled gauge theories, analyzing the spectrum of composite fermions, their interactions, and potential phenomenological implications for composite Higgs models.

Contribution

It introduces fermion fields into bottom-up holographic models of composite Higgs theories, enabling the study of fermionic bound states and their couplings in the Veneziano limit.

Findings

Identification of light fermionic bound states depending on parameters

Discovery of a dense spectrum due to multi-scale dynamics

Observation of dangerously irrelevant operators affecting IR couplings

Abstract

We continue our study of strongly-coupled, approximately scale-invariant gauge theories with a large number of flavours, which provide a suitable ultraviolet completion of the composite-Higgs scenario. We identify the requisite operators to realise partial compositeness of the Standard-Model fermions. In order to compute the spectrum of composite fermionic states, we extend the bottom-up holographic models, which we previously introduced to capture the main features of the non-perturbative dynamics in the Veneziano limit, by adding fermion fields in the bulk. We identify regions in parameter space where some fermionic bound states become light, depending in particular on the number of flavours, the operator scaling dimensions, and the bulk Yukawa couplings. We also observe a dense spectrum of states, when multi-scale dynamics is induced by a large backreaction of bulk scalars on the geometry. Adapting the formalism of the holographic Wilsonian renormalisation group, we study the linear coupling between the composite and elementary fermions, as a function of energy scale. We find that, in some circumstances, the associated operators are dangerously irrelevant: the renormalisation-group flow gives rise to a large linear coupling in the infrared, even when it is irrelevant from the point of view of the ultraviolet fixed point. We finally compute the partially composite spectrum, correlate it with the analysis of the flow, and assess the potential phenomenological implications, e.g. for the top-quark partners.