Remarks on partition functions of topological string theory on generalized conifolds

Abstract

The method of topological vertex for topological string theory on toric Calabi-Yau 3-folds is reviewed. Implications of an explicit formula of partition functions in the "on-strip" case, typically the generalized conifolds, are considered. Generating functions of part of the partition functions are shown to be tau functions of the KP hierarchy. The associated Baker-Akhiezer functions play the role of wave functions, and satisfy $q$-difference equations. These $q$-difference equations represent the quantum mirror curves conjectured by Gukov and Sułkowski.

20 pages, 5 figures, contribution to the proceedings of the RIMS camp-style seminar "Algebraic combinatorics related to Young diagrams and statistical physics" (IIAS, Kyoto, August, 2012); (v2) minor changes including correction of typos

References in corpus (5)

• Chern-Simons-Matter Theory
• Melting Crystal, Quantum Torus and Toda Hierarchy
• A Conjecture on Hodge Integrals
• Quantum Mirror Curves for ${\mathbb{C}}^3$ and the Resolved Confiold
• Radionic Non-uniform Stable Black Strings

Cited by in corpus (4)

• Open string amplitudes of closed topological vertex
• Double nested Hilbert schemes and the local stable pairs theory of curves
• Generalized Ablowitz-Ladik hierarchy in topological string theory
• $q$-Difference Kac-Schwarz Operators in Topological String Theory