Crystal Model for the Closed Topological Vertex Geometry

Abstract

The topological string partition function for the neighbourhood of three spheres meeting at one point in a Calabi-Yau threefold, the so-called 'closed topological vertex', is shown to be reproduced by a simple Calabi-Yau crystal model which counts plane partitions inside a cube of finite size. The model is derived from the topological vertex formalism. This derivation can be understood as 'moving off the strip' in the terminology of hep-th/0410174, and offers a possibility to simplify topological vertex techniques to a broader class of Calabi-Yau geometries. To support this claim a flop transition of the closed topological vertex is considered and the partition function of the resulting geometry is computed in agreement with general expectations.