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We study strongly-coupled, approximately scale-invariant gauge theories,which develop a mass gap in the infrared. We argue that a large number offermion flavours is most suitable to provide an ultraviolet completion for thecomposite Higgs scenario. The holographic approach allows to describe thequalitative features of the non-perturbative dynamics in the Veneziano limit.We introduce new bottom-up holographic models, which incorporate thebackreaction of flavour on the geometry, and show that this can correlate themass gap to the scale of flavour-symmetry breaking. We compute the massspectrum for the various composite bosonic states, and study its dependence onthe scaling dimension of the symmetry-breaking operators, as well as on thenumber of flavours. The different regions with a light dilaton are criticallysurveyed. We carefully assess the domain of validity of the holographicapproach, and compare it with lattice simulations and the Nambu--Jona-Lasiniomodel.

Holographic models of composite Higgs in the Veneziano limit. Part I. Bosonic sector