Abstract
The purpose of this article is to analyze the connection between Eynard–Orantin topological recursion and formal WKB solutions of a -difference equation: with . In particular, we extend the notion of determinantal formulas and topological type property proposed for formal WKB solutions of -differential systems to this setting. We apply our results to a specific -difference system associated to the quantum curve of the Gromov–Witten invariants of for which we are able to prove that the correlation functions are reconstructed from the Eynard–Orantin differentials computed from the topological recursion applied to the spectral curve . Finally, identifying the large x expansion of the correlation functions, proves a recent conjecture made by Dubrovin and Yang regarding a new generating series for Gromov–Witten invariants of .
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