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

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 $C{P}^{N-1}$ 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 $C{P}^{N-1}$ 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.

26 pages

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Cited by in corpus (24)

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• Chiral superfluidity of the quark-gluon plasma
• Local P Violation Effects and Thermalization in QCD: Views from Quantum Field Theory and Holography
• Gauge Field Strength Tensor from the Overlap Dirac Operator
• Correlation and localization properties of topological charge density and the pseudoscalar glueball mass in SU(3) lattice Yang-Mills theory
• Cautionary remarks on the moduli space metric for multi-dyon simulations
• P odd fluctuations and Long Range Order in Heavy Ion Collisions. Deformed QCD as a Toy Model
• Is $N=2$ Large?
• Long range order in gauge theories. Deformed QCD as a toy model
• Classical Limits of Scalar and Tensor Gauge Operators Based on the Overlap Dirac Matrix
• Theta-vacuum and large N limit in CP^{N-1} sigma models
• Small Instantons in $C{P}^1$ and $C{P}^2$ Sigma Models
• Fractionally charged Wilson loops as a probe of $\theta$-dependence in $C{P}^{N-1}$ sigma models: Instantons vs. large N
• Fractional topological charge in $SU(N)$ gauge theories without dynamical quarks
• Nonabelian Strings and Axion
• $\theta$-dependence in the small-$N$ limit of $2d$ $C{P}^{N-1}$ models
• Chiral quark dynamics and topological charge: The role of the Ramond-Ramond U(1) Gauge Field in Holographic QCD
• Topological insulators and the QCD vacuum: the theta parameter as a Berry phase
• On instability of ground states in 2D CP(N-1) and O(N) models at large N
• Tachyonic crystals and the laminar instability of the perturbative vacuum in asymptotically free gauge theories
• Anomaly Inflow and Membrane Dynamics in the QCD Vacuum