We study the Euclidean two-point correlation function G(q),(x) of the topol
ogical, charge density in QCD. A general statement based on reflection posi
tivity 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, th
at contributes to the determination of the physical value of X,. We show ex
plicitly these features of G(q),(x) in a solvable non-trivial continuum mod
el, the two-dimensional CPN-1 model in the large-hi limit. A similar analys
is is done on the lattice. (C) 1999 Elsevier Science B.V. All rights reserv
ed.