SO(N) gauge theories in 2+1 dimensions

Thesis

We calculate the string tensions, mass spectrum, and deconfining temperatures of SO(N) gauge theories in 2+1 dimensions. After a review of lattice field theory, we describe how we simulate the corresponding lattice gauge theories, construct operators to project on to specific states, and extrapolate values to the continuum limit. We discuss how to avoid possible complications such as finite size corrections and the bulk transition.

SO(N) gauge theories have become recently topical since they do not have a fermion sign problem, are orbifold equivalent to SU(N) gauge theories, and share a common large-N limit in their common sector of states with SU(N) gauge theories. This motivates us to compare the physical properties of SO(N) and SU(N) gauge theories between 'group equivalences', which includes Lie algebra equivalences such as SO(6) and SU(4), and particularly a large-N equivalence. We discuss the large-N orbifold equivalence between SO(N) and SU(N) gauge theories, which relates the large-N gauge theories perturbatively. Using large-N extrapolations at fixed 't Hooft coupling, we test to see if SO(N) gauge theories and SU(N) gauge theories share non-perturbative properties at the large-N limit. If these group equivalences lead to similar physics in the gauge theories, then we could imagine doing finite chemical potential calculations that are currently intractable in SU(N) gauge theories by calculating equivalent quantities in the corresponding SO(N) gauge theories.

We show that the SO(N) and SU(N) values match between group equivalences and at the large-N limit.

Authors: Lau, R

• Publication date: 2014
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: Oxford University, UK
• Language: English
• Keywords: SO(N) gauge theories; lattice field theory
• Subjects: Theoretical physics; Elementary particle theory