On the partition sum of the NS five-brane

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.Comment: 35 page

Blurring the picture:Introductions, invasions, extinctions - Biogeography in a global world

Global biogeography and phylogeography have gained importance as research topics in zoology, as attested by the steady increase in the number of journals devoted to this topic and the number of papers published. Yet, in a globalising world, with species reintroductions, invasions of alien species, and large-scale extinctions, unravelling the true biogeographic relationships between areas and species may become increasingly difficult. We present an introduction to the symposium ‘Biogeography: explaining and predicting species distributions in space and time’ held in Amsterdam in 2007, and the resulting papers as published in this special issue, including papers on crustaceans, birds and mammals