swMATH ID: 23722
Software Authors: Gu, Jie; Sulejmanpasic, Tin
Description: High order perturbation theory for difference equations and Borel summability of quantum mirror curves. We adapt the Bender-Wu algorithm C. M. Bender and T. T. Wu, “Anharmonic oscillator. 2: A study of perturbation theory in large order” in [Phys. Rev. D 7, 1620–1636 (1973; doi:1103/PhysRevD.7.1620)] 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.
Homepage: https://link.springer.com/article/10.1007%2FJHEP12%282017%29014
Dependencies: Mathematica; BenderWu
Keywords: nonperturbative effects; resummation; Calabi-Yau threefold; Bender-Wu algorithm; solitons monopoles and instantons; topological strings
Related Software: BenderWu; Mathematica
Cited in: 5 Publications

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