Partition Functions for the Rigid String and Membrane at Any Temperature

Abstract

Exact expressions for the partition functions of the rigid string and membrane at any temperature are obtained in terms of hypergeometric functions. By using zeta function regularization methods, the results are analytically continued and written as asymptotic sums of Riemann-Hurwitz zeta functions, which provide very good numerical approximations with just a few first terms. This allows to obtain systematic corrections to the results of Polchinski et al., corresponding to the limits $T\to 0$ and $T\to \infty$ of the rigid string, and to analyze the intermediate range of temperatures. In particular, a way to obtain the Hagedorn temperature for the rigid membrane is thus found.

20 pages, LaTeX file, UB-ECM-PF 93/8

References in corpus (4)

• Zeta Functions and the Casimir Energy
• High Temperature Partition Function of the Rigid String
• Mellin Transform Techniques for Zeta-Function Resummations
• Effective potential and stability of the rigid membrane

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• On QCD strings beyond non-interacting model