Perturbative and Geometric Analysis of the Quartic Kontsevich Model

Understand

The analogue of Kontsevich's matrix Airy function, with the cubic potential $\operatorname{Tr}\big(\Phi^3\big)$ replaced by a quartic term $\operatorname{Tr}\big(\Phi^4\big)$ with the same covariance, 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.