Crystal Model for the Closed Topological Vertex Geometry

TL;DR

This paper introduces a crystal model that reproduces the topological string partition function for the closed topological vertex in Calabi-Yau threefolds, simplifying calculations and extending applicability.

Contribution

The paper presents a simple Calabi-Yau crystal model derived from the topological vertex formalism, enabling easier computation of partition functions for complex geometries.

Findings

The crystal model accurately reproduces the partition function for the closed topological vertex.

The model simplifies topological vertex techniques for broader Calabi-Yau geometries.

Partition functions remain consistent under flop transitions, validating the model.

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.