PARTITION-FUNCTIONS FOR THE RIGID STRING AND MEMBRANE AT ANY TEMPERATURE

Exact expressions for the partition functions of the rigid string and membrane at any temperature are obtained in terms of hypergeometric fu nctions. By using zeta-function regularization methods, the results ar e analytically continued and written as asymptotic sums of Riemann-Hur witz zeta functions, which provide very good numerical approximations with just a few first terms. This allows us to obtain systematic corre ctions to the results of Polchinski et al., corresponding to the limit s T --> 0 and T --> infinity of the rigid string, and to analyze the i ntermediate range of temperatures. In particular, a way to obtain the Hagedorn temperature for the rigid membrane is thus found.