SU(2) Gluodynamics and HP1 sigma-model embedding: Scaling, Topology and Confinement

TL;DR

This paper explores the topology of SU(2) gauge fields using the HP1 sigma-model embedding, providing new insights into non-perturbative phenomena like confinement, gluon condensate, and topological structures with high numerical precision.

Contribution

It introduces and validates the HP1 embedding method for studying SU(2) gauge topology, offering detailed numerical estimates of key non-perturbative parameters.

Findings

Compatibility of HP1 topological charge with known definitions

Numerical estimate of gluon condensate and quadratic correction

Evidence linking string tension to sign-coherent topological regions

Abstract

We investigate recently proposed HP1 sigma-model embedding method aimed to study the topology of SU(2) gauge fields. The HP1 based topological charge is shown to be fairly compatible with various known definitions. We study the corresponding topological susceptibility and estimate its value in the continuum limit. The geometrical clarity of HP1 approach allows to investigate non-perturbative aspects of SU(2) gauge theory on qualitatively new level. In particular, we obtain numerically precise estimation of gluon condensate and its leading quadratic correction. Furthermore, we present clear evidences that the string tension is to be associated with global (percolating) regions of sign-coherent topological charge. As a byproduct of our analysis we estimate the continuum value of quenched chiral condensate and the dimensionality of regions, which localize the lowest eigenmodes of overlap Dirac operator.