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arXiv · 2106.08368

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

Boris Bychkov·Petr Dunin-Barkowski·Maxim Kazarian·Sergey Shadrin
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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.

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Boris Bychkov, Petr Dunin-Barkowski, Maxim Kazarian, Sergey Shadrin. 2021-06-15. Generalised ordinary vs fully simple duality for $n$-point functions and a proof of the Borot--Garcia-Failde conjecture. https://doi.org/10.1007/s00220-023-04732-7

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