Band structure in Yang-Mills theories

Abstract

We show how Yang-Mills theory on S 3 × 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.

Backreaction issues in axion monodromy and Minkowski 4-forms

“…The coupling of the axion to the 4-form can be understood as a way to decompactify the compact moduli space of the axion, converting a circle in configuration space into an helix. This process of making global a local symmetry has also been recently discussed in a different context in [86], and it is the basis underlying axion monodromy. The large gauge transformation relating equivalent vacua requires now to shift the axion and the flux quanta simultaneously.…”

Role of Bloch waves in baryon-number violating processes

“…Our discussion here follows that in Ref. [28]. Consider a particle moving in a one-dimensional periodic potential with period π, V (µ) = V (µ + nπ), n ∈ Z.…”

“…Comparison between EW theory and QCD[20,28]. The edges of the Bloch pass bands are labeled by (S(A)S(A)),…”

Baryon number violating scatterings in laboratories

“…This periodic potential has a height of 9.1 TeV before the hypercharge coupling is turned on, which will lower it to about 9.0 TeV. Note that the baryon number is different at different integer values of n, indicating that the potential is not that in a circle but truly periodic [25].…”