Irreducible unitary representations of SU(2,2) and the Hyperbolic Higgs model.

Abstract

This thesis consists of two parts: a mathematical and a physical part. In the mathematical part the irreducible unitary representations of a linear connected semisimple group G are studied. We discuss parabolic subgroups, and induce these subgroups to the whole group to get representations on G. We discuss the Langlands classification, which states that any irreducible unitary representation is the unique irreducible quotient of an suitable parabolically induced representation. After that, tools for building discrete series and measuring irreducibility are considered, and an explicit example to find certain irreducible unitary representations of SU(2,2) is discussed.

In the physical part, we build a model which will solve the hierarchy problem of the Standard Model. Before discussing the model itself, we give a reminder of supersymmetry. After the reminder, the model is described. It assumes 5-dimensional supersymmetry, and breaks supersymmetry explicitely by choosing certain Scherk-Schwarz twists. This results in an explicit SU(2,2) symmetry, which is not an irreducible unitary representation.