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

1999/01/31 by Ettore Vicari · 23 citations
Physics and Astronomy · #Charge (physics) #Correlation #Correlation function (quantum field theory) #Euclidean geometry #Function (biology) #High-Energy Particle Collisions Research #Physics of Superconductivity and Magnetism #Quantum Chromodynamics and Particle Interactions #Topological quantum number #Topology (electrical circuits) #hep-lat #hep-th

paper · pdf · doi:10.1016/s0550-3213(99)00297-7

published in Nuclear Physics B 554(1-2), 301-312 (Elsevier BV) · 15 pages, 1 fig. Accepted for publication in Nucl. Phys. B

arxiv created 1999/05/12 · openalex publication_date 1999/08/01 · arxiv updated 2011/08/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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 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 χ_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.

Citations

• Topological susceptibility at zero and finite T in SU(3) Yang-Mills theory
• Axioms for Euclidean Green's functions II
• Scaling and topological charge of a fixed-point action for SU(2) gauge theory
• SU(Nc) gauge theories for all Nc in 3 and 4 dimensions
• Axioms for Euclidean Green's functions

Cited by

• The negativity of the overlap-based topological charge density correlator in pure-glue QCD and the non-integrable nature of its contact part
• Measuring the topological susceptibility in a fixed sector