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

We study the Euclidean two-point correlation function G(q),(x) of the topological, charge density in QCD. A general statement based on reflection positivity tells us that G(q),(x) < 0 for x not equal 0. On the other hand, the topological susceptibility chi(q), = fd(d)xG(q)(x) is a positive quantity. This indicates that G(q),(x) develops a positive contact term at x = 0, that contributes to the determination of the physical value of X,. We show explicitly these features of G(q),(x) in a solvable non-trivial continuum model, the two-dimensional CPN-1 model in the large-hi limit. A similar analysis is done on the lattice. (C) 1999 Elsevier Science B.V. All rights reserved.