Gauge topology and confinement: an update

TL;DR

This paper reviews recent developments in understanding how instanton-dyons contribute to confinement and chiral symmetry breaking, emphasizing their interactions, ensemble behavior, and implications for lattice QCD studies.

Contribution

It summarizes recent analytical and numerical studies on instanton-dyon interactions and their role in confinement and chiral symmetry breaking, including the Dense Dyonic Plasma model.

Findings

Instanton zero modes are small and crucial for lattice simulations.

Instanton-dyons can explain both confinement and chiral symmetry breaking.

High-density dyon ensembles can be analyzed analytically using mean-field approaches.

Abstract

In the instanton ensemble the fermionic zero modes collectivize and break chiral symmetry. Recent studies of resulting zero mode zone confirm its very small width and overall importance for lattice simulations. Confinement however has been related with completely different topological objects, the magnetic monopoles. Instanton constituents -- instanton dyons, discovered at nonzero holonomy by Pierre van Baal and others -- are able to explain both confinement and chiral symmetry breaking. The talk summarizes recent works deriving the instanton-dyon mutual interactions, and statistical studies of their ensemble. At high density the screening is robust enough to do it analytically, in the mean-field-type approach: we call this limit Dense Dyonic Plasma (DDP). Above $T_c$ the classical interaction between the dyons induce strong correlations and should be studied by direct numerical simulations. Those works are now in progress.