  This note is the written version of a talk which was presented at the Cargese
2002 summer school. It gives a brief introduction to the paper hep-th/0205281,
written in collaboration with R. Dijkgraaf and E. Verlinde. In this paper, we
calculate the euclidean partition function of the type IIA NS five-brane
wrapped on an arbitrary Calabi-Yau space in a double-scaling decoupling limit
and in the presence of a flat RR 3-form background field. The result is the
product of a theta function, coming from the classical fluxes of the self-dual
tensor field, and a factor representing the quantum contributions. The quantum
factor turns out to be related to topological B-model string amplitudes, and
both factors satisfy a holomorphic anomaly equation. The result can teach us
more about little string theories and about instanton corrections to
four-dimensional effective quantities.
