Blobbed topological recursion of the quartic Kontsevich model II: $\mathrm{Genus}=0$ (with an appendix by Maciej Dołęga)

Abstract

We prove that the genus-0 sector of the quartic analogue of the Kontsevich model is completely governed by an involution identity which expresses the meromorphic differential ${\omega }_{0,n}$ at a reflected point $\iota z$ in terms of all ${\omega }_{0,m}$ with $m\le n$ at the original point $z$. We prove that the solution of the involution identity obeys blobbed topological recursion, which confirms a previous conjecture about the quartic Kontsevich model.