Hagedorn transition, vortices and D0 branes: Lessons from 2+1 confining strings

TL;DR

This paper investigates the confining-deconfining phase transition in a 3D gauge theory, revealing that the transition involves decay into D0 branes and vortex condensation, with implications for understanding string behavior and monopole dynamics.

Contribution

It provides a detailed world-sheet and field theory analysis of the phase transition mechanism involving D0 branes and vortices in the Georgi-Glashow model.

Findings

Transition involves decay into D0 branes at lower than Hagedorn temperature.

Vortices on the world-sheet represent D0 brane world-lines.

Hagedorn transition corresponds to monopole binding transition.

Abstract

We study the behaviour of Polyakov confining string in the Georgi-Glashow model in three dimensions near confining-deconfining phase transition described in hep-th/0010201. In the string language, the transition mechanism is the decay of the confining string into D0 branes (charged W bosons of the Georgi-Glashow model). In the world-sheet picture the world-lines of heavy D0 branes at finite temperature are represented as world-sheet vortices of a certain type, and the transition corresponds to the condensation of these vortices. We also show that the ``would be'' Hagedorn transition in the confining string (which is not realized in our model) corresponds to the monopole binding transition in the field theoretical language. The fact that the decay into D0 branes occurs at lower than the Hagedorn temperature is understood as the consequence of the large thickness of the confining string and finite mass of the $D0$ branes.