Band Structure in Yang-Mills Theories

Understand

We show how Yang-Mills theory on $S^3\times R$ can exhibit a spectrum with continuous bands if coupled either to a topological 3-form gauge field, or to a dynamical axion with heavy Peccei-Quinn scale.

• The basic mechanism consists in associating winding histories to a bosonic zero mode whose role is to convert a circle in configuration space into a helix.
• The zero mode is, respectively, the holonomy of the 3-form field or the axion momentum.
• In these models different theta sectors coexist but are not mixed by local operators.