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

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

1999-01-12

arxiv.org/abs/hep-lat/9901008v2

Nucl.Phys.B554:301-312,1999

Physics

High Energy Physics

High Energy Physics - Lattice

15 pages, 1 fig. Accepted for publication in Nucl. Phys. B

Scientific paper

10.1016/S0550-3213(99)00297-7

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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