Deconfinement in Yang-Mills theory through toroidal compactification with deformation

TL;DR

This paper develops a semi-classical approach to study the deconfinement transition in Yang-Mills theory by using a double-trace deformation and toroidal compactification, connecting it to two-dimensional field theories and statistical physics models.

Contribution

It introduces a novel deformation technique that allows the deconfinement transition to be analyzed in a semi-classical regime, linking four-dimensional Yang-Mills to two-dimensional theories.

Findings

Deconfinement transition driven by electric-magnetic perturbation competition.

Thermodynamics at large N matches ordinary Yang-Mills.

Supports magnetic component scenario of quark-gluon plasma.

Abstract

We introduce field theory techniques through which the deconfinement transition of four-dimensional Yang-Mills theory can be moved to a semi-classical domain where it becomes calculable using two-dimensional field theory. We achieve this through a double- trace deformation of toroidally compactified Yang-Mills theory on R2 \times S1_L \times S1_{\beta}. At large N, fixed-L, and arbitrary {\beta}, the thermodynamics of the deformed theory is equivalent to that of ordinary Yang-Mills theory at leading order in the large N expansion. At fixed-N, small L and a range of {\beta}, the deformed theory maps to a two-dimensional theory with electric and magnetic (order and disorder) perturbations, analogs of which appear in planar spin-systems and statistical physics. We show that in this regime the deconfinement transition is driven by the competition between electric and magnetic perturbations in this two-dimensional theory. This appears to support the scenario proposed by Liao and Shuryak regarding the magnetic component of the quark-gluon plasma at RHIC.