Composite Higgs Models: a new holographic approach

We revisit the construction of the composite Higgs models in a context of the bottom-up holographic approach. The soft wall framework is under consideration imposing the translation of the $4D$ global symmetry breaking characteristic to the new strongly interacting sector in the $5D$ bulk. The focus stays on the minimal $SO(5)\to SO(4)$ breaking pattern. The $5D$ model has a specific form inspired by the effective models of QCD, representing a generalized sigma model coupled both to the composite resonances and to the SM gauge bosons. The latter are treated as external $4D$ sources and conceptually develop no propagation into the bulk. The holographic description allows for the consideration of spin one and spin zero resonances. The resulting spectrum leads in a natural way to a variety of new composite resonances, four of which represent the massless Goldstone bosons. Existing experimental constraints on the electroweak precision parameters permit to accommodate vector and scalar resonances with masses in the $1 - 2$ TeV range without difficulties, but higher masses are possible too. Moreover, for the SM gauge fields holography provides relevant vacuum polarization amplitudes and mixing with composite resonances. Further considering higher order correlation functions we can formulate semi-quantitative predictions for the effective couplings and cross-sections. These provide additional restrictions that are currently being investigated.