Blobbed topological recursion of the quartic analogue of the Kontsevich model

Raimar Wulkenhaar (U M√ľnster)

Oct 14. 2020, 10:15 — 11:00

We provide strong evidence for the conjecture that the analogue of Kontsevich’s matrix Airy function, with the cubic potential Tr(\Phi^3 ) replaced by a quartic term Tr(\Phi^4), obeys the blobbed topological recursion of Borot and Shadrin. We identify in the quartic Kontsevich model three families of correlation functions for which we establish interwoven loop equations. One family consists of symmetric meromorphic differential forms \omega_{g,n} labelled by genus and number of marked points of a complex curve. We reduce the solution of all loop equations to a straightforward but lengthy evaluation of residues. In all evaluated cases, the $\omega_{g,n} consist of a part with poles at ramification points which satisfies the universal formula of topological recursion, and of a part holomorphic at ramification points for which we provide an explicit residue formula.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Higher Structures Emerging from Renormalisation - partially postponed (Online Workshop)
Pierre Clavier (U of Haut-Alsace)
Kurusch Ebrahimi-Fard (NTNU, Trondheim)
Peter K. Friz (TU Berlin)
Harald Grosse (U of Vienna)
Dominique Manchon (U Clerment Auvergne)
Sylvie Paycha (U of Potsdam)
Sylke Pfeiffer (U of Potsdam)