Generalised Ordinary vs Fully Simple Duality for n-Point Functions and a Proof of the Borot–Garcia-Failde Conjecture

Source abstract

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.