  It is generally accepted that consistent coupling to quantum gravity implies
that any low energy free parameter is in reality the vacuum expectation value
of some local quantum field. In this note we present a modest attempt to prove
this general claim using as key example the theta parameter of QCD and the
Peccei-Quinn axion solution of the strong CP problem. The gravitational
emergence of the local axion field associated with the superselection theta
parameter is worked out using as basic ingredients the quantum representation
of classical geometries in terms of coherent states and the interpretation of
the theta QCD superselection rule in quantum information terms as the lack of a
quantum reference frame for topological charge. The formal connection with the
model independent axion in string theory is briefly discussed.
