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

Abstract

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 ≠ 0. On the other hand, the topological susceptibility χ q = ∫ d 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 χ q . We show explicitly these features of G q ( x) in a solvable non-trivial continuum model, the two-dimensional C P N−1 model in the large- N limit. A similar analysis is done on the lattice.