Band structure in Yang-Mills theories

We show how yang-mills theory on s3 × 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 θ sectors coexist and are only mixed by (non-local) volume operators. our analysis sheds light on, and extends seiberg’s proposal for modifying the topological sums in quantum field theories. it refutes a recent claim that b + l violation at lhc is unsuppressed.