UC San Diego

Since the development of the standard model over 40 years ago, one of the chief endeavors of particle physics has been to understand the Higgs sector of the theory. Still experimentally undetected despite great efforts, the Higgs sector remains a mystery, and ideas of what lies beyond have flourished. The aim of the research described here has been to explore non-perturbatively ideas of greatest interest which are within reach of current non- perturbative methods and resources and beyond the current reach of rigorous perturbative investigation. The first is the relationship between the Higgs boson mass and the energy scale of new phenomena expected to appear at higher energies due to a peculiar property of Higgs models known as triviality. The second is nearly conformal gauge theory and its role in the possible explanation of the Higgs as a composite state, again linking to new phenomena at higher energies, namely extended technicolor. The imminent advent of the Large Hadron Collider makes the discovery and understanding of new physics at higher energies a tangible possibility. In the likely event that new phenomena results and producing the next generation of theories