Article,
Touring the Hagedorn ridge
(2004)
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.
