Linear confinement in the partially-deconfined phase

TL;DR

This paper investigates the partially-deconfined phase in large-N Yang-Mills theory, proposing that a flux tube forms in the confined sector leading to linear confinement, supported by lattice simulations and theoretical analysis.

Contribution

It introduces the concept of linear confinement in the partially-deconfined phase and provides analytic and numerical evidence supporting this mechanism.

Findings

Flux tube formation in the confined sector.

Linear confinement potential with size-independent string tension.

Confirmation through lattice gauge theory simulations.

Abstract

We consider the partially-deconfined saddle of large-$N$ pure Yang-Mills theory lying between confined and deconfined phases, in which the color degrees of freedom split into confined and deconfined sectors. Based on the microscopic mechanism of deconfinement, we argue that a flux tube is formed in the confined sector and a linear confinement potential is generated. The string tension should not depend on the size of the confined sector. We provide evidence by studying the finite-temperature strong-coupling lattice gauge theory. In particular, we make analytic predictions assuming linear confinement in the confined sector, and then confirm these by numerical simulations. We discuss some implications of the conjecture to QCD and holography.