Abstract
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.
Highlights
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
It refutes a recent claim that B + L violation at LHC is unsuppressed
The question is whether this strategy can be implemented within local quantum field theory
Summary
To fully specify the model we must still state whether the symmetry under discrete translations, q → q + n, is global or gauged.1 In the former case the particle lives on the real line and the potential has an infinite number of local minima labelled by n ∈ Z, while in the latter it lives on a circle and V has a unique minimum which we may choose to be at q = 0. If we use as reference the non-compact theory with θ = 0, gauging the Z symmetry has the effect of projecting onto the sector with quasi-momentum equal to θ. One may gauge a subgroup {q → q +nN |n ∈ Z} of the global symmetry and project onto N states with -spaced quasi-momenta in each energy band.
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