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

Vicari, Ettore (1999) The Euclidean two-point correlation function of the topological charge density. Nuclear Physics B - Proceedings Supplements, 554 (1-2). pp. 301-312. ISSN 1873-3832

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\neq 0 $. On the other hand the topological susceptibility $\chi_q=\int d^d x G_q(x)$ is a positive quantity. This indicates that $G_q(x)$ developes a positive contact term at $x=0$, that contributes to the determination of the physical value of $\chi_q$. We show explicitly these features of $G_q(x)$ in a solvable nontrivial continuum model, the two-dimensional $CP^{N-1}$ model in the large-N limit. A similar analysis is done on the lattice.

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