BWDifference 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 Referenced in: 5 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year High order perturbation theory for difference equations and Borel summability of quantum mirror curves. Zbl 1383.81267Gu, Jie; Sulejmanpasic, Tin 2017 all top 5 Referenced by 10 Authors 3 Mariño, Marcos 2 Gu, Jie 2 Sulejmanpasic, tin 1 Codesido, Santiago 1 Duan, Zhihao 1 Emery, Yoan 1 Hatsuda, Yasuyuki 1 Ronzani, Massimiliano 1 Schiappa, Ricardo 1 Zakany, Szabolcs Referenced in 2 Serials 4 Journal of High Energy Physics 1 Annales Henri Poincaré Referenced in 5 Fields 5 Quantum theory (81-XX) 5 Relativity and gravitational theory (83-XX) 2 Algebraic geometry (14-XX) 2 Partial differential equations (35-XX) 1 Several complex variables and analytic spaces (32-XX) Referencing Publications by Year