The Negativity of the Overlap-Based Topological Charge Density Correlator in Pure-Glue QCD and the Non-Integrable Nature of its Contact Part

TL;DR

This study investigates the lattice two-point function of topological charge density in pure-glue QCD using overlap operators, confirming non-positivity at non-zero distances and the non-integrable contact part, supporting the existence of a brane-like topological structure.

Contribution

It provides the first detailed lattice calculation of the topological charge density correlator with overlap operators, confirming its non-positivity and non-integrable contact behavior in the continuum limit.

Findings

Correlator is non-positive at non-zero distances in the continuum limit.

The positive core size is approximately twice the lattice spacing near the continuum.

The correlator exhibits divergent short-distance behavior and a non-integrable contact part.

Abstract

We calculate the lattice two-point function of topological charge density in pure-glue QCD using the discretization of the operator based on the overlap Dirac matrix. Utilizing data at three lattice spacings it is shown that the continuum limit of the correlator complies with the requirement of non-positivity at non-zero distances. For our choice of the overlap operator and the Iwasaki gauge action we find that the size of the positive core is ~2a (with a being the lattice spacing) sufficiently close to the continuum limit. This result confirms that the overlap-based topological charge density is a valid local operator over realistic backgrounds contributing to the QCD path integral, and is important for the consistency of recent results indicating the existence of a low-dimensional global brane-like topological structure in the QCD vacuum. We also confirm the divergent short-distance behavior of the correlator, and the non-integrable nature of the associated contact part.