Topological recursion, symplectic duality, and generalized fully simple maps

TL;DR

This paper develops a framework connecting topological recursion and symplectic duality, providing explicit formulas and proving recursion for generalized fully simple maps.

Contribution

It introduces symplectic dual spectral curves and establishes a formula linking their topological recursion outputs to the original curve.

Findings

Explicit formula for n-point functions via symplectic duality

Proof of topological recursion for generalized fully simple maps

New connections between spectral curves and map enumeration

Abstract

For a given spectral curve, we construct a family of symplectic dual spectral curves for which we prove an explicit formula expressing the $n$-point functions produced by the topological recursion on these curves via the $n$-point functions on the original curve. As a corollary, we prove topological recursion for the generalized fully simple maps generating functions.