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We compute the partition function of the supersymmetric two-dimensionalEuclidean black hole geometry described by the SL(2,R)/U(1) superconformalfield theory. We decompose the result in terms of characters of the N=2superconformal symmetry. We point out puzzling sectors of states besidesfinding expected discrete and continuous contributions to the partitionfunction. By adding an N=2 minimal model factor of the correct central chargeand projecting on integral N=2 charges we compute the partition function of thebackground dual to little string theory in a double scaling limit. We show theprecise correspondence between this theory and the background for NS5-branes ona circle, due to an exact description of the background as a null gauging ofSL(2,R) x SU(2). Finally, we discuss the interplay between GSO projection andtarget space geometry.Comment: JHEP class, 35 pages, no figures; v2: minor changes, typos corrected,  published versio

The partition function of the supersymmetric two-dimensional black hole and little string theory