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arXiv · 1604.01690

Quantization condition from exact WKB for difference equations

Amir-Kian Kashani-Poor
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Abstract

A well-motivated conjecture states that the open topological string partition function on toric geometries in the Nekrasov-Shatashvili limit is annihilated by a difference operator called the quantum mirror curve. Recently, the complex structure variables parameterizing the curve, which play the role of eigenvalues for related operators, were conjectured to satisfy a quantization condition non-perturbative in the NS parameter $\hbar$. Here, we argue that this quantization condition arises from requiring single-valuedness of the partition function, combined with the requirement of smoothness in the parameter $\hbar$. To determine the monodromy of the partition function, we study the underlying difference equation in the framework of exact WKB.

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Amir-Kian Kashani-Poor. 2016-08-26. Quantization condition from exact WKB for difference equations. https://doi.org/10.1007/jhep06(2016)180

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