Green's Functions and Topological Configurations

TL;DR

This paper explores the relationship between topological configurations and Green's functions in Yang-Mills theory, using lattice gauge theory to analyze their connection and effects on non-perturbative phenomena like confinement.

Contribution

It demonstrates that Green's functions remain qualitatively consistent across different topological configurations, suggesting a unified underlying physics.

Findings

Green's functions are stable under smearing and cooling.

Qualitative properties of Green's functions persist in the almost (anti-)self-dual domain.

Supports the idea that topological and Green's function views are interconnected.

Abstract

There are, among others, currently two important views on the non-perturbative structure of Yang-Mills theory. One is through topological configurations and one is through Green's functions, in particular their (asymptotic) infrared behavior. Based on both views, various scenarios for confinement, chiral symmetry breaking and other non-perturbative effects have been developed. However, if both views are correct then they can only be different aspects of the same underlying physics, and it must be possible to relate them. After discussing the current status of the understanding of this connection, smeared and cooled configurations in lattice gauge theory are used to determine the properties of Green's functions in the low-momentum regime. It is found that the qualitative properties are essentially unchanged compared to results on unsmeared configurations. This is also the case when the configurations are smeared sufficiently strongly to reach the almost (anti-)self-dual domain.