  We study the Type IIA NS five-brane wrapped on a Calabi-Yau manifold X in a
double-scaled decoupling limit. We calculate the euclidean partition function
in the presence of a flat RR 3-form field. The classical contribution is given
by a sum over fluxes of the self-dual tensor field which reduces to a
theta-function. The quantum contributions are computed using a T-dual IIB
background where the five-branes are replaced by an ALE singularity. Using the
supergravity effective action we find that the loop corrections to the free
energy are given by B-model topological string amplitudes. This seems to
provide a direct link between the double-scaled little strings on the
five-brane worldvolume and topological strings. Both the classical and quantum
contributions to the partition function satisfy (conjugate) holomorphic anomaly
equations, which explains an observation of Witten relating topological string
theory to the quantization of three-form fields.
