Anatomy of Deconfinement

TL;DR

This paper explores the phenomenon of partial deconfinement in gauge theories, linking it to spontaneous gauge symmetry breaking and black hole formation, with implications for understanding deconfinement in QCD and holography.

Contribution

It demonstrates the existence of a partially deconfined phase in weakly coupled gauge theories and interprets it as spontaneous gauge symmetry breaking, providing new insights into deconfinement mechanisms.

Findings

Identification of a partially deconfined phase with M/N growing from 0 to 1

Interpretation of partial deconfinement as spontaneous gauge symmetry breaking

Connection between gauge symmetry breaking and black hole formation in gravity duals

Abstract

In the weak coupling limit of ${\rm SU}(N)$ Yang-Mills theory and the ${\rm O}(N)$ vector model, explicit state counting allows us to demonstrate the existence of a partially deconfined phase: $M$ of $N$ colors deconfine, and $\frac{M}{N}$ gradually grows from zero (confinement) to one (complete deconfinement). We point out that the mechanism admits a simple interpretation in the form of spontaneous breaking of gauge symmetry. In terms of the dual gravity theory, such breaking occurs during the formation of a black hole. We speculate whether the breaking and restoration of gauge symmetry can serve as an alternative definition of the deconfinement transition in theories without center symmetry, such as QCD. We also discuss the role of the color degrees of freedom in the emergence of the bulk geometry in holographic duality.