Gauge-Higgs Unification Theories on 5D Orbifolds

In the first chapter we present some general concepts related to theories with extra dimensions adopting the KK perspective. In particular we report the general form of the action for scalar, fermion and gauge fields on a 5D interval with generic warped metric. At the same time we briefly discuss the boundary conditions which are allowed in these theories. Afterwards we present the general features of orbifold compactifications including a review of Scherk-Schwarz boundary conditions and Wilson lines. In chapter 2 we give a comprehensive presentation of the holographic approach. In the first part of the chapter we discuss the general framework, focusing in particular on the non-trivial case of gauge fields. In the second part we present three interesting applications of the holographic procedure. We begin with the computation of the treelevel holographic action for a generic 5D model, showing how it can be used to compute the one-loop Higgs effective potential in GHU theories. Then we use holography to obtain the Chiral Perturbation Theory (xPT) Lagrangian in Holographic QCD. As a last, more theoretical, application, we study the consequences of the introduction of a Chern-Simons (CS) term into a 5D gauge theory. The last three chapters are devoted to the study of 5D GHU theories compactified on the orbifold 8 1 /Z2. We begin with a review of the simplest implementation of the GHU idea which gives rise to the semi-realistic model of [15]. In particular we will discuss the general framework of this model pointing out its appealing features and its shortcuts. In chapter 4 we show how the problems of the previously considered model can be solved by assuming a breaking of the Lorentz symmetry along the fifth dimension and introducing the Z2 mirror symmetry. Furthermore, we will present a detailed study of this theory from both a qualitative and a quantitative point of view, determining the constraints on the parameter space which arise from the EW precision measurements and giving an estimate of the amount of fine-tuning of the model. As side remarks, we briefly discuss the presence of a viable DM candidate in the theory and we suggest a possible mechanism which could give origin to a spontaneous breaking of the Lorentz invariance in a purely 5D context. Finally, in chapter 5, we study the properties of GHU models at finite temperature. First of all we discuss the general features of the finite-temperature Higgs effective potential at one loop, showing that an Electroweak Phase Transition (EWPT) is always present in such models at a temperature of order 1/(2nR). Then we specialize our analysis to the models presented in chapters 3 and 4, and we perform a detailed study of the phase transition using analytic and numerical techniques. As a last issue, in section 5.3, we give some evidence of the stability of the finite-temperature one-loop potential in GHU models showing that the leading higher-loop corrections are not very relevant up to temperatures well above the EWPT. We also include at the end some, quite technical, appendices. In the first one we present a more formal derivation of the gauge-fixing procedure employed in the holographic approach of chapter 2. In the next appendix, we show how it is possible to handle boundary terms and localized fields within the holographic description and we exemplify this possibility by treating the toy model of a scalar with boundary mass terms on a warped space. In appendix C we collect some useful formulae needed to compute the holographic action for the AdS5 and flat space cases. In appendix D we give the decomposition of the most relevant SU(3) representations in terms of multiplets of the SU(2) x U(l) subgroup. This decomposition results useful in the study of the GHU models presented in chapters 3, 4 and 5. In appendix E another application of the holographic approach is given, namely we show how one can compute the distortion of the ZbLbL vertex (see section 4.4.1) in a simplified toy model. In appendix F we analyze the localization of the fermion zero-modes in the model of chapter 4. In the last appendix the explicit form of the finite-temperature one-loop Higgs potential is reported. In particular we collect various equivalent formulae by which one express the finite-temperature contributions to the potential.