String distributions above the Hagedorn energy density

Abstract

The formalism for discussing energy and charge distribution functions in the microcanonical ensemble is presented and applied to strings. This yields information of direct physical significance in string statistical mechanics. Above the Hagedorn energy density the free string gas exhibits a number of interesting features. For toroidal compactification, the distribution of the total energy among strings of various energies depends upon the number of noncompact spatial dimensions $d$. For $d=0$ the energy is distributed uniformly among strings at all energy scales, while for $d\ensuremath{\ge}3$ a single string captures most of the energy. The imposition of conservation laws does not alter this qualitative picture. We show that the $d=1$ and $d=2$ cases are qualitatively different from the others.