Open issues in confinement, for the lattice and for center vortices

TL;DR

This paper discusses unresolved issues in confinement mechanisms in QCD, proposing new models and lattice simulation tests for understanding Wilson loops, the Lüscher term, and the role of center vortices and gluons.

Contribution

It introduces a polymer model for vortices, explores dualities with gluon chains, and suggests lattice studies and gauge-fixing methods to advance understanding of confinement.

Findings

A conjecture that minimal-area law and Lüscher term arise from vortex ensembles.

Proposal of lattice simulations to test vortex models.

Discussion of duality between gluon chains and vortex condensates.

Abstract

Topological confinement by center vortices does not immediately explain either a minimum-area law for non-planar Wilson loops or the L\"uscher term. I conjecture that both a minimal-area law and a L\"uscher term arise in a confinement model of random ensembles of vortices with no propagating gluons (a polymer model), and propose their test by polymer-like lattice simulations. I also consider the role of dynamically-massive gluons propagating from one point to another on a Wilson loop, and conjecture an approximate duality between the gluon-chain model and a condensate of center vortices with nexuses (magnetic monopoles) propagating on the vortex surfaces. I explore the old fishnet model, updated to deal with propagating massive QCD gluons, and argue that it leads to a surface tension and therefore a L\"uscher term, as expressed through an effective action of the Dirichlet form that describes tension. I propose various lattice studies of non-planar Wilson loops to investigate such issues. Finally, in a different vein I urge the lattice community to study gauge-fixing to the background-field Feynman gauge, which will yield the gauge-invariant off-shell Greens functions of the pinch technique.