Advances in Theoretical and Mathematical Physics
Volume 10 (2006)
The vertex on a strip
Pages: 317 – 343
We demonstrate that for a broad class of local Calabi--Yau geometries built around a string of $\IP^1$'s --- those whose toric diagrams are given by triangulations of a strip --- we can derive simple rules, based on the topological vertex, for obtaining expressions for the topological string partition function in which the sums over Young tableaux have been performed. By allowing non-trivial tableaux on the external legs of the corresponding web diagrams, these strips can be used as building blocks for more general geometries. As applications of our result, we study the behavior of topological string amplitudes under flops, as well as check Nekrasov's conjecture in its most general form.