Abstract
ABSTRACT String theories give rise to divergent expressions for the Helmholtz free energy at temperatures above the Hagedorn temperature. Although this may signal some phase transition, we show that, regarding these divergences as tachyonic and spurious in nature, they can be eliminated from thermodynamical quantities by the use of regularization schemes and analytic continuation prescriptions. Generically, for closed strings, we obtain finite expressions which develop however an imaginary part above the Hagedorn temperature. For open strings, on the other hand, dilatonic divergences survive regularization. Imaginary parts are interpreted as decay rate of the unstable perturbative phase.
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