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

TL;DR

This paper suggests that the shape of the topological density correlation function in pure-glue QCD is primarily determined by the space-time geometry of a double-sheet structure, implying a homogeneous global topological fluctuation model.

Contribution

It introduces the idea that the correlation function shape is governed by space-time folding, with the distribution within sheets affecting only magnitude, proposing a homogeneous double membrane as a collective degree of freedom.

Findings

Shape of correlation function is reproduced by sign of topological density.

Topological fluctuations may be modeled as a global space-filling double membrane.

Distribution within sheets influences magnitude, not shape.

Abstract

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.