Note on supersymmetric Yang-Millls thermodynamics - art. no. 106010

The thermodynamics of supersymmetric Yang-Mills theories is studied by comp uting the two-loop correction to the canonical free energy and to the equat ion of state for theories with 16, 8, and 4 supercharges in any dimension 4 less than or equal to d less than or equal to 10, and in two dimensions at finite volume. In the four-dimensional case we also evaluate the first non analytic contribution in the 't Hooft coupling to the free energy, arising from the resummation of ring diagrams. To conclude, we discuss some applica tions to the study of the Hagedom transition in string theory in the contex t of Matrix strings and speculate on the possible physical meaning of the t ransition. [S0556-2821(99)08618-X].