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I discuss the infrared mass spectrum of strongly-coupled gauge theories, thatinduce the Higgs as a composite pseudo-Nambu-Goldstone boson. The set ofcomposite states accompanying the Higgs is determined by the symmetries of thetheory. Here we estimate their mass spectrum by non-perturbative techniquesinspired by QCD, as well as by exploiting gauge-gravity duality. 1 CompositeHiggs: motivations and relevant energy scales As the Large Hadron Collider (LHC)did not find new states significantly coupled to the Standard Model (SM) belowthe TeV scale, any SM extension by such heavy states suffers from a littlehierarchy problem, as the mass of the scalar Higgs boson lies close to the 100GeV scale. Still, some SM extensions have the potential to address the bighierarchy between the TeV scale and the Planck scale. One possibility is toavoid elementary scalar fields, and assume the observed Higgs is a compositeobject, with a compositeness scale f 1 TeV. This scenario requires a strongly-coupled sector, whose spectrum generically includes several additional compositestates besides the Higgs. The mass of the lowest-lying states cannot exceed ∼4πf , and some could be significantly lighter and within the LHC reach. Definitepredictions for the mass spectrum require to specify the strongly-coupled theoryin the ultraviolet (UV). Here we will assume it is a gauge theory of fermions,that confines in the infrared. We will estimate its mass spectrum in some well-defined approximations, by employing non-perturbative techniques inspired by QCD1) , as well as gauge-gravity duality techniques 2). In models where the Higgsis a pseudo-Nambu-Goldstone boson (pNGB) the electroweak scale, v 246 GeV, isinduced in two steps. The theory has a global (flavour) symmtry G F , that isspontaneously broken to a subgroup H F at the scale f. The electroweak symmetrySU (2) L × U (1) Y is embedded in 91