Quantizing Weierstrass
Mathematical Physics
2018-08-06 v2 High Energy Physics - Theory
Algebraic Geometry
math.MP
Abstract
We study the connection between the Eynard-Orantin topological recursion and quantum curves for the family of genus one spectral curves given by the Weierstrass equation. We construct quantizations of the spectral curve that annihilate the perturbative and non-perturbative wave-functions. In particular, for the non-perturbative wave-function, we prove, up to order hbar^5, that the quantum curve satisfies the properties expected from matrix models. As a side result, we obtain an infinite sequence of identities relating A-cycle integrals of elliptic functions and quasi-modular forms.
Keywords
Cite
@article{arxiv.1610.00225,
title = {Quantizing Weierstrass},
author = {Vincent Bouchard and Nitin K. Chidambaram and Tyler Dauphinee},
journal= {arXiv preprint arXiv:1610.00225},
year = {2018}
}
Comments
40 pages. v2: published version (improved presentation)