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arXiv · 1709.00854

High order perturbation theory for difference equations and Borel summability of quantum mirror curves

Jie Gu·Tin Sulejmanpasic
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Abstract

We adapt the Bender-Wu algorithm to solve perturbatively but very efficiently the eigenvalue problem of "relativistic" quantum mechanical problems whose Hamiltonians are difference operators of the exponential-polynomial type. We implement the algorithm in the function BWDifference in the updated Mathematica package BenderWu. With the help of BWDifference, we survey quantum mirror curves of toric fano Calabi-Yau threefolds, and find strong evidence that not only are the perturbative eigenenergies of the associated 1d quantum mechanical problems Borel summable, but also that the Borel sums are exact.

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Jie Gu, Tin Sulejmanpasic. 2017-09-04. High order perturbation theory for difference equations and Borel summability of quantum mirror curves. https://doi.org/10.1007/jhep12(2017)014

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