COUNTING CLOSED STRING STATES IN A BOX

The computation of the microcanonical density of states for a string g as in a finite volume needs a one by one count because of the discrete nature of the spectrum. We present a way to do it using geometrical a rguments in phase space. We take advantage of this result in order to obtain the thermodynamical magnitudes of the system. We show that the results for an open universe exactly coincide with the infinite volume limit of the expression obtained for the gas in a box. For any finite volume the Hagedorn temperature is a maximum one, and the specific he at is always positive. We also present a definition of pressure compat ible with R-duality seen as an exact symmetry, which allows us to make a study on the physical phase space of the system. Besides a maximum temperature the gas presents an asymptotic pressure. (C) 1997 Elsevier Science B.V.