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

Alexander Hock; Raimar Wulkenhaar

doi:10.4171/aihpd/198

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

Alexander Hock
University of Oxford, Oxford, UK
Raimar Wulkenhaar
University of Münster, Münster, Germany

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

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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 $ω_{0, n}$ at a reflected point $ιz$ in terms of all $ω_{0, m}$ 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.

Cite this article

Alexander Hock, Raimar Wulkenhaar, Blobbed topological recursion of the quartic Kontsevich model II: $Genus = 0$ (with an appendix by Maciej Dołęga). Ann. Inst. Henri Poincaré Comb. Phys. Interact. (2024), published online first

DOI 10.4171/AIHPD/198