Linear confinement in the partially-deconfined phase

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 for the case of 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.

Automated summary

We study the partially-deconfined saddle in large-N pure Yang-Mills theory, which lies between the confined and deconfined phases and splits the color degrees of freedom into confined and deconfined sectors. By analyzing the mechanism of deconfinement, we propose the formation of a flux tube and the generation of a linear confinement potential in the confined sector. We provide evidence for this conjecture through analytic predictions and numerical simulations in the case of finite-temperature strong-coupling lattice gauge theory, and discuss its implications in QCD and holography.