The Hagedorn Transition, Deconfinement and the AdS/CFT Correspondence

TL;DR

This paper explores the relationship between the Hagedorn transition in string theory and the deconfinement transition in Yang-Mills theory using the AdS/CFT correspondence, revealing a topology change linked to black hole formation.

Contribution

It introduces a modified Witten model with supersymmetry-breaking boundary conditions to connect Hagedorn and deconfinement transitions via a topology-changing phase transition.

Findings

Identification of a Hagedorn-like transition in the model

Observation of Wilson loop behavior above the transition

Connection between black hole formation and deconfinement

Abstract

A connection between the Hagedorn transition in string theory and the deconfinement transition in (non-supersymmetric) Yang-Mills theory is made using the AdS/CFT correspondence. We modify the model of zero temperature QCD proposed by Witten by compactifying an additional space-time coordinate with supersymmetry breaking boundary conditions thus introducing a finite temperature in the boundary theory. There is a Hagedorn-like transition associated with winding modes around this coordinate, which signals a topology changing phase transition to a new AdS/Schwarzschild blackhole where this coordinate is the time coordinate. In the boundary gauge theory time like Wilson loops acquire an expectation value above this temperature.