Re-Identifying the Hagedorn Transition

The Hagedorn transition in string theory is normally associated with an exponentially rising density of states, or equivalently with the existence of a thermal string winding mode which becomes tachyonic above a specific temperature. However, the details of the Hagedorn transition turn out to depend critically on the precise manner in which a zero-temperature string theory is extrapolated to finite temperature. In this paper, we argue that for broad classes of closed string theories, the traditional Hagedorn transition is completely absent when the correct extrapolation is used. However, we also argue that there is an alternative ``re-identified'' Hagedorn transition which is triggered by the thermal winding excitations of a different, ``effective'' tachyonic string ground state. These arguments allow us to re-identify the Hagedorn temperature for heterotic strings. Moreover, we find that all tachyon-free closed string models in ten dimensions share the same (revised) Hagedorn temperature, resulting in a universal Hagedorn temperature for both Type II and heterotic strings. We also comment on the possibility of thermal spin-statistics violations at the Planck scale.