Deformation and Quantisation Condition of the \(\mathcal {Q}\)-Top Recursion

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 \(\mathcal {Q}\) $\mathcal{Q}$ -top recursion. We then show a coincidence between a deformation condition and a quantisation condition in terms of the \(\mathcal {Q}\) $\mathcal{Q}$ -top recursion on a degenerate elliptic curve. We also discuss a relation to the corresponding Nekrasov–Shatashivili effective twisted superpotential.