Thermal Duality Transformations and the Canonical Ensemble: The Deconfining Long String Phase Transition

TL;DR

This paper formulates the statistical mechanics of strings in the canonical ensemble, demonstrating T^2 free energy growth at high temperatures, ruling out exponential divergences, and identifying a Wilson loop as a phase transition order parameter.

Contribution

It provides a first principles formulation compatible with T-duality, analyzes high-temperature behavior, and introduces a Wilson loop as an order parameter for string-scale phase transitions.

Findings

T^2 growth in free energy at high temperatures

No exponential divergence in one-loop free energy

Wilson-Polyakov-Susskind loop as a phase transition indicator

Abstract

We give a first principles formulation of the equilibrium statistical mechanics of strings in the canonical ensemble, compatible with the Euclidean timelike T-duality transformations that link the six supersymmetric string theories in pairs. We demonstrate that each exhibits a T^2 growth in the free energy at high temperatures far above the string scale. We verify that the low energy field theory limit of our expression for the string free energy reproduces the expected T^{10} growth when the contribution from massive string modes is suppressed. In every case, heterotic, type I, and type II, we can definitively rule out the occurrence of an exponential divergence in the one-loop string free energy above some critical temperature. Finally, we identify a macroscopic loop amplitude in the type I string theories which yields the expectation value of a single Wilson-Polyakov-Susskind loop in the low energy finite temperature supersymmetric gauge theory limit, an order parameter for a thermal phase transition at a string scale temperature. We point out that precise computations can nevertheless be carried out on either side of the phase boundary by using the low energy finite temperature supersymmetric gauge theory limits of the pair of thermal dual string theories, type IB and type I'. Note Added (Sep 2005).