Heterotic Type I Strings at High Temperature

TL;DR

This paper demonstrates the finiteness of high-temperature limits in heterotic and Type I superstrings, identifies a thermal deconfinement transition at the self-dual temperature, and explores related worldsheet formalism aspects.

Contribution

It provides new insights into the high-temperature behavior of heterotic and Type I superstrings, including phase transition evidence and duality relations.

Findings

High-temperature limits are finite and convergent for heterotic and Type I strings.

Evidence of a thermal deconfinement phase transition at the self-dual temperature.

Discontinuity in free energy and potential indicates deconfined gluon phase.

Abstract

We show that the high temperature limits of the heterotic E8xE8 and Spin(32)/Z2 strings and their Type I A/B superstring duals are finite and convergent. The Hagedorn growth of the degeneracies in the string mass level expansion is suppressed by an exponential linear in the mass level number for both heterotic strings, and suppressed by the exponential of the negative square root of the mass level number for the Type IB superstring. However, in the massless gauge field theoretic limit of the Type IB open and closed superstring, we find clear evidence for the thermal deconfinement phase transition at the self-dual temperature by examining the annulus graph alone. Above the self-dual temperature, there is a discontinuity in the first derivative with respect to temperature of both the free energy, and the heavy quark potential, leading to a deconfined thermal gluon ensemble, with universal 1/r potential, and temperature dependent corrections, as predicted by Luscher and Weisz. A number of essential aspects of the worldsheet formalism of the heterotic strings are derived in an appendix, deducing thereby the O8-D0-D8brane Type IA duals of all of the heterotic CHL island universe moduli spaces.