  We develop a bottom-up holographic model that provides the dual description
of a strongly coupled field theory, in which the spontaneous breaking of an
approximate global symmetry yields the SO(5)/SO(4) coset relevant to minimal
composite-Higgs models. The gravity background is completely regular and
smooth, and has an end of space that mimics confinement on the field theory
side. We add to the gravity description a set of localised boundary terms, that
introduce additional symmetry-breaking effects, capturing those that would
result from coupling the dual strongly coupled field theory to an external,
weakly coupled sector. Such terms encapsulate the gauging of a subgroup of the
global $SO(5)$ symmetry of the dual field theory, as well as additional
explicit symmetry-breaking effects. We show how to combine spurions and gauge
fixing and how to take the appropriate limits, so as to respect gauge
principles and avoid violations of unitarity.
  The interplay of bulk and boundary-localised couplings leads to the breaking
of the SO(5) symmetry to either its SO(4) or SO(3) subgroup, via vacuum
misalignment. In field theory terms, the model describes the spontaneous
breaking of a SO(4) gauge symmetry to its SO(3) subgroup. We expose the
implications of the higgsing phenomenon by computing the spectrum of
fluctuations of the model, which we interpret in four-dimensional field-theory
terms, for a few interesting choices of parameters. We conclude by commenting
on the additional steps needed to build a realistic composite Higgs model.
