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\leq 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.