Quantum Mirror Curves for ${\mathbb{C}}^3$ and the Resolved Confiold

Abstract

We establish a conjecture of Gukov and Sułkowski in the following three cases: Lambert curve for Hurwitz numbers, framed mirror curve of ${\mathbb{C}}^3$, and the framed mirror curve of the resolved conifold.

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Cited by in corpus (6)

• Quantum curves for Hitchin fibrations and the Eynard-Orantin theory
• Topological recursion and a quantum curve for monotone Hurwitz numbers
• Quantum curves for the enumeration of ribbon graphs and hypermaps
• Remarks on partition functions of topological string theory on generalized conifolds
• $q$-Difference Kac-Schwarz Operators in Topological String Theory
• Quantum curve and bilinear Fermionic form for the orbifold Gromov-Witten theory of $\mathbb{P}[r]$