Deconfinement and the Hagedorn transition in string theory

We introduce a new definition of the thermal partition function in string t heory. With this new definition, the thermal partition functions of all of the string theories obey thermal duality relations with self-dual Hagedorn temperature beta (2)(H) = 4 pi (2)alpha (1). A beta --> beta (2)(H)/beta tr ansformAtion maps the type I theory into a new string theory (type (I) over tilde) with thermal Dp-branes, spatial hypersurfaces supporting a p-dimens ional finite temperature non-Abelian Higgs-gauge theory for p less than or equal to 9. We demonstrate a continuous phase transition in the behavior of the static heavy quark-antiquark potential for small separations r(*)(2) m uch less than alpha (1) transitioning through a precise inverse power law a t a critical temperature T-D = T(H)r(*)/(2 alpha')(1/2)pi.