Band Structure in Yang-Mills Theories

TL;DR

This paper explores how Yang-Mills theories on $S^3 imes R$ can develop continuous spectral bands through coupling to topological fields, providing insights into topological sectors and challenging claims about baryon-lepton violation at LHC.

Contribution

It introduces a mechanism linking winding histories to zero modes, extending Seiberg's proposals and clarifying the suppression of $B+L$ violation in quantum field theories.

Findings

Spectral bands arise in Yang-Mills theories with topological couplings.

Different theta sectors coexist without mixing via local operators.

Refutes the claim of unsuppressed $B+L$ violation at LHC.

Abstract

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. 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.