Lattice Gauge Fields Topology Uncovered by Quaternionic sigma-model Embedding

TL;DR

This paper introduces a novel approach to analyze SU(2) gauge fields topology using quaternionic sigma-models, revealing localized topological structures distinct from instantons and demonstrating universal properties across lattice spacings.

Contribution

The authors develop a new method linking SU(2) gauge theory with quaternionic sigma-models to compute topological charge density directly from sigma-model fields.

Findings

Topological charge is localized in four-dimensional regions not corresponding to instantons.

The method is compatible with overlap-based definitions for thermalized vacuum configurations.

Universal properties of topological density distribution are observed across different lattice spacings.

Abstract

We investigate SU(2) gauge fields topology using new approach, which exploits the well known connection between SU(2) gauge theory and quaternionic projective sigma-models and allows to formulate the topological charge density entirely in terms of sigma-model fields. The method is studied in details and for thermalized vacuum configurations is shown to be compatible with overlap-based definition. We confirm that the topological charge is distributed in localized four dimensional regions which, however, are not compatible with instantons. Topological density bulk distribution is investigated at different lattice spacings and is shown to possess some universal properties.