An algebraic approach to a quartic analogue of the Kontsevich model

Schürmann, Jörg; Wulkenhaar, Raimar

Abstract

We consider an analogue of Kontsevich’s matrix Airy functionwhere the cubic potential Tr(φ3) is replaced by a quartic term Tr(φ4). Cumulants of the resulting measure are known to decompose into cycle types forwhich a recursive system of equations can be established. We develop a new, purely algebraic geometrical solution strategy for the two initial equations ofthe recursion, based on properties of Cauchy matrices. These structures led in subsequent work to the discovery that the quartic analogue of the Kontsevichmodel obeys blobbed topological recursion.