Dominance of Sign Geometry and the Homogeneity of the Fundamental Topological Structure

We propose and support the possibility that the shape of topological density 2–point function in pure–glue QCD is crucially, and possibly entirely, determined by the space–time folding (geometry) of the double–sheet sign–coherent structure of Ref. [1], while the distribution of topological density within individual sheets only determines the overall magnitude of the correlator at finite physical distances. A specific manifestation of this, discussed here, is that the shape of the correlation function (encoding e.g. the masses of pseudoscalar glueballs) is reproduced upon the replacement q(x) → sgn(q(x)), i.e. by considering the double sheet of the same space–time geometry but with constant magnitude of topological density. Combined with previous results on the fundamental topological structure, this suggests that a collective degree of freedom describing topological fluctuations of QCD vacuum can be viewed as a global space-filling homogeneous double membrane. Selected possibilities for practical uses of this are discussed.