Touring the Hagedorn Ridge

TL;DR

This paper explores the Hagedorn regime in string theories, proposing a topology change in spacetime as the underlying cause of phase transitions, and relates these phenomena to black hole and gauge theory transitions.

Contribution

It introduces a novel perspective linking string phase transitions to topology changes via an Euclidean string/black hole correspondence, supported by toy model studies.

Findings

Thermal winding mode condensation triggers phase transitions.

Topology change in spacetime underlies the phase transition mechanism.

Connections established between string theory, black holes, and gauge theories.

Abstract

We review aspects of the Hagedorn regime in critical string theories, from basic facts about the ideal gas approximation to the proposal of a global picture inspired by general ideas of holography. It was suggested that the condensation of thermal winding modes triggers a first-order phase transition. We propose, by an Euclidean analogue of the string/black hole correspondence principle, that the transition is actually related to a topology change in spacetime. Similar phase transitions induced by unstable winding modes can be studied in toy models. There, using T-duality of supersymmetric cycles, one can identify a topology change of the Gregory--Laflamme type, which we associate with large-N phase transitions of Yang--Mills theories on tori. This essay is dedicated to the memory of Ian Kogan.