Investigating the conformal window of SU(N) gauge theories

Thesis

In this thesis we are concerned with the existence of infrared fixed points and the conformal window for gauge theories with fermions. We are particularly interested in those theories that are candidates for walking technicolor. We discuss the background of technicolor and the techniques relevant to a theoretical understanding of the conformal window. Following this we extend the ideas of metric confinement and causal analyticity to theories with fermions in non-fundamental representations. We use these techniques to, respectively, provide a lower bound on the lower end of the conformal window and to provide a measure of perturbativity. As well as analytic calculations we use lattice techniques to investigate two particular candidate theories for walking technicolor - SU(2) with two adjoint fermions and with six fundamental fermions. We use Schrodinger Functional techniques to investigate the running of the theory across a wide range of scales. We measure both the running of the coupling and an estimator for the fermion mass anomalous dimension, $gamma$. We find that both theories are consistent with an infrared fixed-point. However, paying particular attention to our error estimates, we are unable to absolutely confirm their existence. This is a not unexpected result for SU(2) with two adjoint fermions but is rather surprising for SU(2) with only six fundamental fermions. In the region where we are consistent with a fixed point we find $0.05

Authors: Pickup, T

• Publication date: 2011
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: Oxford University, UK
• Language: English
• Keywords: lattice gauge theory; technicolor; conformal window
• Subjects: Elementary particle theory; Particle physics; Theoretical physics