Deformation and quantisation condition of the $\mathcal{Q}$-top recursion

Abstract

We consider a deformation of a family of hyperelliptic refined spectral curves and investigate how deformation effects appear in the hyperelliptic refined topological recursion as well as the $\mathcal{Q}$-top recursion. We then show a coincidence between a deformation condition and a quantisation condition in terms of the $\mathcal{Q}$-top recursion on a degenerate elliptic curve. We also discuss a relation to the corresponding Nekrasov-Shatashivili effective twisted superpotential.

Minor corrections. Accepted version by Annales Henri Poincare

References in corpus (4)

• Irregular Liouville correlators and connection formulae for Heun functions
• Topological expansion of beta-ensemble model and quantum algebraic geometry in the sectorwise approach
• Perturbative connection formulas for Heun equations
• Quantum curves from refined topological recursion: the genus 0 case

Cited by in corpus (1)

• $\mathfrak{b}$-Hurwitz numbers from refined topological recursion