Topological Charge Membranes in 2D and 4D Gauge Theory

TL;DR

This paper investigates the structure of topological charge in 2D and 4D gauge theories, revealing long-range coherence along lower-dimensional regions and connecting these findings to similar phenomena in QCD.

Contribution

It demonstrates the presence of coherent topological charge regions in 2D models and relates these to 3D sheets observed in 4D QCD, highlighting a common surface-like structure.

Findings

Long-range topological charge coherence in 2D models

Identification of surface-like topological structures in gauge theories

Connection between 2D and 4D topological charge phenomena

Abstract

Local topological charge structure in the 2D CP(N-1) sigma models is studied using the overlap Dirac operator. Long-range coherence of topological charge along locally 1D regions in 2D space-time is observed. We discuss the connection between these results and the recent discovery of coherent 3D sheets of topological charge in 4D QCD. In both cases, coherent regions of topological charge form along surfaces of approximmate codimension 1.