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Coherent Topological Charge Structure in $CP^{N-1}$ Models and QCD

Saeed Ahmad·Jonathan T. Lenaghan·H. B. Thacker
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Abstract

In an effort to clarify the significance of the recent observation of long-range topological charge coherence in QCD gauge configurations, we study the local topological charge distributions in two-dimensional $CP^{N-1}$ sigma models, using the overlap Dirac operator to construct the lattice topological charge. We find long-range sign coherence of topological charge along extended one-dimensional structures in two-dimensional spacetime. We discuss the connection between the long range topological structure found in $CP^{N-1}$ and the observed sign coherence along three-dimensional sheets in four-dimensional QCD gauge configurations. In both cases, coherent regions of topological charge form along membrane-like surfaces of codimension one. We show that the Monte Carlo results, for both two-dimensional and four-dimensional gauge theory, support a view of topological charge fluctuations suggested by Luscher and Witten. In this framework, the observed membranes are associated with boundaries between ``k-vacua,'' characterized by an effective local value of $θ$ which jumps by $\pm 2π$ across the boundary.

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Saeed Ahmad, Jonathan T. Lenaghan, H. B. Thacker. 2005-09-21. Coherent Topological Charge Structure in $CP^{N-1}$ Models and QCD. https://doi.org/10.1103/physrevd.72.114511

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