Coherent topological charge structure in CPN-1 models and QCD -: art. no. 114511

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 CPN-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 CPN-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 membranelike 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 +/- 2 pi across the boundary.