From scalar fields on quantum spaces to blobbed topological recursion

TL;DR

This paper explores the connection between scalar field models on noncommutative geometries and blobbed topological recursion, highlighting their implications in algebraic and enumerative geometry through exact solutions and Dyson-Schwinger equations.

Contribution

It introduces a novel link between quantum field theory on noncommutative spaces and blobbed topological recursion, expanding the understanding of their mathematical structure.

Findings

Exact solutions of Dyson-Schwinger equations for the $mbda\u03c6^4$-model

Establishment of a relationship between noncommutative quantum field models and topological recursion

Insights into algebraic and enumerative geometry via quantum field theoretic methods

Abstract

We review the construction of the $\lambda\phi^4$-model on noncommutative geometries via exact solutions of Dyson-Schwinger equations and explain how this construction relates via (blobbed) topological recursion to problems in algebraic and enumerative geometry.