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

Jie Gu, Tin Sulejmanpasic
2017 Journal of High Energy Physics  
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
more » ... s of the associated 1d quantum mechanical problems Borel summable, but also that the Borel sums are exact.
doi:10.1007/jhep12(2017)014 fatcat:pyjczbik7zdrxjsmugydvh4dpa