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.

arXiv commentMinor corrections. Accepted version by Annales Henri Poincare

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Cited by in corpus (1)

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