This thesis is organized as follows. Chapter 2 gives an introduction to the subject starting with a discussion of composite Higgs models where the Higgs arises as a PGB. This is followed by introducing the Minimal Composite Higgs Model (MCHM) as a promising example. A simple fact regarding deconstructed models is then addressed as a link to theories with an extra dimension. Chapter 3 is devoted to certain 5D theories and their holographic interpretation. In the first part of this chapter the holographic method for gauge fields is discussed. This method is then applied to the gauge sector of the minimal composite Higgs model in 5D flat space with boundary kinetic terms. A comparison with the more standard KK approach is made afterwards. Introduction to the notion of
holography for fermions will be the final part if this chapter. In chapter 4 we introduce three composite-Higgs/GHU models in flat space and study in detail their compatibility with EWPT. The gauge sector of these models is that of the MCHM described previously, and they differ in the way the SM fermions are embedded in complete multiplets of the bulk gauge group. In the first model, known as MCHM_5, fermions are embedded in four fundamental representations. In the second model fermions are embedded in two fundamentals, while in the third model they are embedded in one adjoint representation. Fermionic kinetic terms are also introduced on the UV boundary in the last two models. Details of the computation of the 1-loop corrections to the Z ̄bLbL vertex are collected in Appendix A. In Appendix B after a short introduction to EWPT, 1-loop computation of electroweak precision observables as well as the χ^2 fit performed for our three models are explained in detail.
