  We study the semi-classical limit of the reflection coefficient for the
SL(2,R)_k/U(1) CFT. For large k, the CFT describes a string in a Euclidean
black hole of 2-dimensional dilaton-gravity, whose target space is a cigar with
an asymptotically linear dilaton. This sigma-model description is weakly
coupled in the large k limit, and we investigate the saddle-point expansion of
the functional integral that computes the reflection coefficient. As in the
semi-classical limit of Liouville CFT, we find that one must complexify the
functional integral and sum over complex saddles to reproduce the limit of the
exact reflection coefficient. Unlike Liouville, the SL(2,R)_k/U(1) CFT admits
bound states that manifest as poles of the reflection coefficient. To reproduce
them in the semi-classical limit, we find that one must sum over configurations
that hit the black hole singularity, but nevertheless contribute to the
saddle-point expansion with finite action.
