Euclidean Time Formulation for the Superstring Ensembles: Perturbative Canonical Ensemble with Neveu-Schwarz B Field Backgrounds

TL;DR

This paper develops a Euclidean time formulation for superstring ensembles, demonstrating finite high-temperature limits, suppressed Hagedorn growth, and evidence for a thermal deconfinement transition at the self-dual temperature.

Contribution

It introduces a new Euclidean time approach for superstring ensembles, analyzing high-temperature behavior and phase transitions with detailed derivations and duality insights.

Findings

High-temperature limits of heterotic and Type I superstrings are finite and convergent.

Hagedorn growth is exponentially suppressed in the mass level expansion.

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

Abstract

The lengthy discussion and derivations given in this paper have been corrected, and completed with additional results and greater simplicity. 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.