Refined topological recursion revisited -- properties and conjectures

Publication date: 3 May 2023

Abstract: For any (possibly singular) hyperelliptic curve, we give the definition of a hyperelliptic refined spectral curve and the hyperelliptic refined topological recursion, generalising the formulation for a special class of genus-zero curves by Kidwai and the author, and also improving the proposal by Chekhov and Eynard. Along the way, we uncover a fundamental geometric structure underlying the hyperelliptic refined topological recursion and investigate its properties -- parts of which remain conjectural due to computational difficulties. Moreover, we establish a new recursion valid in the so-called Nekrasov-Shatashivili limit and prove existence of the corresponding quantum curve.

Has companion code repository: https://github.com/jaime-varela/arxivFilterEmailer

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