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.

26 pages, 7 figures; references added, classical part of flop analysis corrected and expanded

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Cited by in corpus (19)

• A & B model approaches to surface operators and Toda theories
• Crystal Melting and Toric Calabi-Yau Manifolds
• Non-Lagrangian Theories from Brane Junctions
• Topological strings and 5d T_N partition functions
• Refined Topological Vertex, Cylindric Partitions and the U(1) Adjoint Theory
• Instantons on ALE spaces and orbifold partitions
• Seiberg Duality, 5d SCFTs and Nekrasov Partition Functions
• Deformed boson-fermion correspondence, Q-bosons, and topological strings on the conifold
• Wall-crossing, free fermions and crystal melting
• Wall Crossing As Seen By Matrix Models
• Instantons, Quivers and Noncommutative Donaldson-Thomas Theory
• Non-compact Topological Branes on Conifold
• Trinion Conformal Blocks from Topological strings
• Open string amplitudes of closed topological vertex
• Topological String on Toric CY3s in Large Complex Structure Limit
• Non Planar Topological 3-Vertex Formalism
• Refined open topological strings revisited
• $q$-Difference Kac-Schwarz Operators in Topological String Theory
• Periodic Schur Process, Cylindric Partitions and N=2* Theory