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We study a 5D bottom-up holographic model that is expected to describe thedynamics of the minimal composite Higgs model characterized by a $SO(5)\toSO(4)$ global symmetry breaking pattern. We assume that the fundamental degreesof freedom are scalars transforming under some representation of $SO(5)$ andsubject to some unspecified strong interactions. The holographic descriptionpresented here is inspired by previous studies performed in the context of QCDand it allows for the consideration of spin one and spin zero resonances. Theresulting spectrum leads in a natural way to a variety of resonances. Namely,those transforming under the unbroken $SO(4)$ subgroup exhibit an exactdegeneracy between the two Regge trajectories of vector and scalar channels,while the resonances with quantum numbers in the $SO(5)/ SO(4)$ coset lie on atrajectory of (heavier) spin one states and a non-degenerated one of scalarresonances where the four lowest lying ones are massless. These correspond tothe four Goldstone bosons in 4D associated to the global symmetry breakingpattern. Restrictions derived from the experimental constraints (Higgscouplings, $S$ parameter, etc.) are then implemented and we conclude that themodel is able to accommodate vector and scalar resonances with masses in therange 1 TeV to 2 TeV without encountering phenomenological difficulties.Extension to generic models characterized by the breaking pattern $SO(N)\toSO(N^\prime<N)$ is straightforward.

Holographic description of $SO(5) \rightarrow SO(4)$ composite Higgs model