2005/09/21 by Saeed Ahmad, Jonathan Lenaghan, Jonathan T. Lenaghan +1 · 4 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Charge (physics) #Combinatorics #Gauge theory #Lattice gauge theory #Mathematics #Particle physics theoretical and experimental studies #Physics #Quantum #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Topological order #Topological quantum number #Topology (electrical circuits) #hep-lat #hep-th
paper · pdf · doi:10.1103/physrevd.72.114511
published as Phys.Rev. D72 (2005) 114511 · 26 pages
arxiv created 2005/09/21 · openalex publication_date 2005/12/22 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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\ensuremath-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\ensuremath-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 L"uscher and Witten. In this framework, the observed membranes are associated with boundaries between ``k-vacua,'' characterized by an effective local value of \ensuremathθ which jumps by \ifmmode±\else\textpm\fi2\ensuremathπ across the boundary.