  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.
