Open string amplitudes of closed topological vertex

Abstract

The closed topological vertex is the simplest ``off-strip'' case of non-compact toric Calabi-Yau threefolds with acyclic web diagrams. By the diagrammatic method of topological vertex, open string amplitudes of topological string theory therein can be obtained by gluing a single topological vertex to an ``on-strip'' subdiagram of the tree-like web diagram. If non-trivial partitions are assigned to just two parallel external lines of the web diagram, the amplitudes can be calculated with the aid of techniques borrowed from the melting crystal models. These amplitudes are thereby expressed as matrix elements, modified by simple prefactors, of an operator product on the Fock space of 2D charged free fermions. This fermionic expression can be used to derive $q$-difference equations for generating functions of special subsets of the amplitudes. These $q$-difference equations may be interpreted as the defining equation of a quantum mirror curve.

latex2e, package amsmath,amssymb,amsthm,graphicx, 10 figures; (v2) Typos are corrected, the beginning of "Introduction'' is slightly expanded, and "Remark 5" is added in the end of Section 6

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Cited by in corpus (6)

• Toda hierarchies and their applications
• Refined open topological strings revisited
• Cubic Hodge integrals and integrable hierarchies of Volterra type
• $q$-Difference Kac-Schwarz Operators in Topological String Theory
• Integrable structures of specialized hypergeometric tau functions
• Three-partition Hodge integrals and the topological vertex