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

TL;DR

This paper investigates the long-range topological charge coherence in $CP^{N-1}$ models and QCD, revealing membrane-like structures of codimension one that are linked to topological fluctuations and vacua boundaries.

Contribution

It demonstrates the presence of extended topological structures in $CP^{N-1}$ models and connects these findings to similar structures observed in QCD, supporting a membrane-based view of topological charge fluctuations.

Findings

Long-range sign coherence of topological charge along one-dimensional structures.

Membrane-like surfaces of codimension one form topological regions.

Results support the boundary between k-vacua with $ heta$ jumps of $ imes 2\pi$.

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 $\theta$ which jumps by $\pm 2\pi$ across the boundary.