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

We compute the partition function of the supersymmetric two-dimensional euclidean black hole geometry described by the SL(2,ℝ)/U(1) superconformal field theory. We decompose the result in terms of characters of the N = 2 superconformal symmetry. We point out puzzling sectors of states besides finding expected discrete and continuous contributions to the partition function. By adding an N = 2 minimal model factor of the correct central charge and projecting on integral N = 2 charges we compute the partition function of the background dual to little string theory in a double scaling limit. We show the precise correspondence between this theory and the background for NS5-branes on a circle, due to an exact description of the background as a null gauging of SL(2, ℝ) × SU(2). Finally, we discuss the interplay between GSO projection and target space geometry.