Quantum gravity forces the QCD theta parameter to emerge as the vev of a local axion field through coherent-state representations of geometry and a quantum-information interpretation of topological-charge superselection.
Thus, at least superficially the TSG approach is not enough to generate the local axion field
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Gravity, Superselection Rules and Axions
Quantum gravity forces the QCD theta parameter to emerge as the vev of a local axion field through coherent-state representations of geometry and a quantum-information interpretation of topological-charge superselection.