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

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Referee this paper: arXiv:1412.3736 by Shyamoli Chaudhuri

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We derive the Euclidean time formulation for the equilibrium canonical ensemble of the type IIA and type IIB superstrings, and the $SO(32)$ heterotic string. We compactify on $R^8\times T^2$, and twist by the Neveu-Schwarz sector antisymmetric 2-form B-field potential, spontaneously breaking supersymmetry at low temperatures, while preserving the tachyon free low-energy gravitational field theory limit. We verify that the super partners of the massless dilaton-graviton multiplet obtain a mass which is linear in the temperature. In addition, we show that the free energy for the superstring canonical ensemble at weak coupling is always strongly convergent in the ultraviolet, high-temperature, regime dominated by the highest mass level number states. We derive the precise form of the exponential suppression as a linear power of the mass level, which erases the exponential Hagedorn growth of the degeneracies as the square root of mass level number. Finally, we close a gap in previous research giving an unambiguous derivation of the normalization of the one-loop vacuum energy density of the $SO(32)$ perturbative heterotic string theory. Invoking the $O(32)$ type IB--heterotic strong-weak duality, we match the normalization of the one loop vacuum energy densities of the T-dual O(32) type IA open and closed string with that of the $SO(32)$ heterotic string on $R^9\times S^1$, for values of the compactification radius, $R_{[O(32)]}, R_{IB}>>\sqrt{\alpha'}$, with $R_{IA}<\sqrt{\alpha'}$. We show that the type IA thermal solitonic winding spectrum is a simple model for finite temperature pure QCD, transitioning above the critical duality phase transformation temperature to the deconfined ensemble of thermally excited IB gluons.

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paper authored Dec 11, 2014
edited Mar 29, 2015

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