Euclidean time formulation for the superstring ensembles: Perturbative canonical ensemble with Neveu-SchwarzB-field backgrounds

Abstract

We derive the Euclidean time formulation for the equilibrium canonical ensemble of the type IIA and type IIB superstrings, and the spinð32Þ=Z 2 heterotic string. We compactify on R 8 × 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 spinð32Þ=Z 2 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 spinð32Þ=Z 2 heterotic string on R 9 × S 1 , for values of the compactification radius, R ½Oð32Þ , R IB ≫ α 01=2 , with R IA < α 01=2 . 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. 1 There are some typos in both [2] and [3,4] in the expressions for the string free energy, but they do not take away from the pioneering elegance of these early papers. PHYSICAL REVIEW D 90, 126005 (2014) 1550-7998=2014=90 (12)=126005(34) 126005-1

Unruh Duality and Maximum Acceleration in String Theory

“…But note that the value of the self-dual temperature comes from the T-duality transformation formula, equation (18), that holds as long as the target space has an compactified Euclidean time direction. Also, there are thermal string constructions free of Hagedorn instabilities (see for example [35,36,37,38]) and the arguments of the previous section can be applied for the bosonic sector of them. Also, there could be potential applications to Euclidean type II * theories 5 (see [39] and references therein), as they can be seen as T-dual to type II strings (though in the time-like direction).…”