Partition Functions for the Rigid String and Membrane at Any Temperature

Details Partition Functions for the Rigid String and Membrane at Any Temperature Partition Functions for the Rigid String and Membrane at Any Temperature

1993-04-19

arxiv.org/abs/hep-th/9304071v1

Phys.Rev.D48:1757-1767,1993

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1103/PhysRevD.48.1757

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 $T\rightarrow 0$ and $T\rightarrow \infty$ 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.

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