A NOVEL REPRESENTATION FOR THE FREE-ENERGY IN STRING THEORY AT NONZERO TEMPERATURE

A novel representation - in terms of a Laurent series - for the free e nergy of string theory at non-zero temperature is constructed. The exa mples of open bosonic, open supersymmetric and closed bosonic strings are studied in detail. In all these cases the Laurent series represent ation for the free energy is obtained explicitly. It is shown that the Hagedorn temperature arises in this formalism as the convergence cond ition (specifically, the radius of convergence) of the corresponding L aurent series. Some prospects for further applications are also discus sed. In particular, an attempt to describe string theory above the Hag edorn temperature - via Borel analytical continuation of the Laurent s eries representation - is provided.