Intersection theory of the complex quartic Kontsevich model

TL;DR

This paper connects the correlation functions of the complex quartic Kontsevich model with intersection numbers on moduli spaces, illustrating the application of topological recursion in a physically motivated setting.

Contribution

It provides a detailed example of how correlation functions in a specific quantum field theory relate to intersection theory and topological recursion, unifying various conventions and notations.

Findings

Explicit expansion of correlation functions in terms of intersection numbers

Application of Chekhov-Eynard-Orantin topological recursion to the model

Unified notation for different conventions in the literature

Abstract

We expand correlation functions of the Langmann-Szabo-Zarembo (LSZ) model in terms of intersection numbers on the moduli space of complex curves. This provides an explicit, physically motivated example for the expansion of correlation functions generated by Chekhov-Eynard-Orantin topological recursion. To this end, we unify notation as well as different conventions present in the literature and use a set of moduli of the spectral curve adapted to the physically motivated model. The presentation focuses on an illustrative, step-by-step comprehension of the work.