Perturbative and Geometric Analysis of the Quartic Kontsevich Model

Johannes Branahl ; Alexander Hock ; Raimar Wulkenhaar

Symmetry, integrability and geometry: methods and applications, Tome 17 (2021)

Résumé

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.

Détail

Keywords: Dyson–Schwinger equations, perturbation theory, topological recursion.
Mots-clés : exact solutions

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