How to Extrapolate A String Model to Finite Temperature: Interpolations and Implications for the Hagedorn Transition

摘要

In this paper, we discuss the important question of how to extrapolate agiven zero-temperature string model to finite temperature. It turns out thatthis issue is surprisingly subtle, and we show that many of the standardresults require modification. For concreteness, we focus on the case of theten-dimensional SO(32) heterotic string, and show that the usualfinite-temperature extrapolation for this string is inconsistent at the levelof a proper worldsheet theory. We then derive the proper extrapolation, and inthe process uncover a universal Hagedorn temperature for all tachyon-freeclosed string theories in ten dimensions --- both Type II and heterotic. As wediscuss, these results are not in conflict with the well-known exponentialgrowth in the degeneracies of string states in such models. This writeup is aconcise summary of our recent paper hep-th/0505233, here presented using a``bottom-up'' approach based on determining self-consistent finite-temperatureextrapolations of zero-temperature string models. Some new results andobservations are also added.