The Euclidean two-point correlation function of the topological charge density

We study the Euclidean two-point correlation function Gq(x) of the topological charge density in QCD. A general statement based on reflection positivity tells us that Gq(x) < 0 for x ≠ 0. On the other hand, the topological susceptibility χq = ∫ ddxGq(x) is a positive quantity. This indicates that Gq(x) develops a positive contact term at x 0, that contributes to the determination of the physical value of χq. We show explicitly these features of Gq(x) in a solvable non-trivial continuum model, the two-dimensional CPN-1 model in the large-N limit. A similar analysis is done on the lattice