Generalised ordinary vs fully simple duality for $n$-point functions and a proof of the Borot--Garcia-Failde conjecture

Abstract

We study a duality for the $n$-point functions in VEV formalism that we call the ordinary vs fully simple duality. It provides an ultimate generalisation and a proper context for the duality between maps and fully simple maps observed by Borot and Garcia-Failde. Our approach allows to transfer the algebraicity properties between the systems of $n$-point functions related by this duality, and gives direct tools for the analysis of singularities. As an application, we give a proof of a recent conjecture of Borot and Garcia-Failde on topological recursion for fully simple maps.

arXiv comment25 pages; minor corrections

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Cited by in corpus (6)

• On the $x$-$y$ Symmetry of Correlators in Topological Recursion via Loop Insertion Operator
• KP integrability through the $x-y$ swap relation
• Degenerate and irregular topological recursion
• $x-y$ duality in Topological Recursion for exponential variables via Quantum Dilogarithm
• Symplectic duality for topological recursion
• Topological recursion, symplectic duality, and generalized fully simple maps