  We study the phenomenology of partially composite-Higgs models where
electroweak symmetry breaking is dynamically induced, and the Higgs is a
mixture of a composite and an elementary state. The models considered have
explicit realizations in terms of gauge-Yukawa theories with new strongly
interacting fermions coupled to elementary scalars and allow for a very SM-like
Higgs state. We study constraints on their parameter spaces from vacuum
stability and perturbativity as well as from LHC results and find that
requiring vacuum stability up to the compositeness scale already imposes
relevant constraints. A small part of parameter space around the classically
conformal limit is stable up to the Planck scale. This is however already
strongly disfavored by LHC results. In different limits, the models realize
both (partially) composite-Higgs and (bosonic) technicolor models and a
dynamical extension of the fundamental Goldstone-Higgs model. Therefore, they
provide a general framework for exploring the phenomenology of composite
dynamics.
