  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) x SU(2). Finally, we discuss the interplay between GSO projection and
target space geometry.
