# Perturbative and Geometric Analysis of the Quartic Kontsevich Model

December 04, 2020

The analogue of Kontsevich's matrix Airy function, with the cubic potential
$\mathrm{Tr}(\Phi^3)$ replaced by a quartic term $\mathrm{Tr}(\Phi^4)$,
provides a toy model for quantum field theory in which all correlation
functions can be computed exactly and explicitly. In this paper we show that
distinguished polynomials of correlation functions, themselves given by quickly
growing series of Feynman ribbon graphs, sum up to much simpler and highly
structured expressions. These expressions are deeply connected with meromorphic
forms conjectured to obey blobbed topological recursion. Moreover, we show how
the exact solutions permit to explore critical phenomena in the Quartic
Kontsevich Model.

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