Complete solution of the LSZ Model via Topological Recursion

TL;DR

This paper demonstrates that the LSZ model, a noncommutative quantum field theory represented as a complex matrix model, can be exactly solved using topological recursion, revealing its integrability properties.

Contribution

It introduces a novel approach to prove the LSZ model's solvability through topological recursion and compares it with related models like Grosse-Wulkenhaar.

Findings

LSZ model obeys topological recursion

Dyson-Schwinger equations lead to loop equations

Comparison with Grosse-Wulkenhaar model highlights differences

Abstract

We prove that the Langmann-Szabo-Zarembo (LSZ) model with quartic potential, a toy model for a quantum field theory on noncommutative spaces grasped as a complex matrix model, obeys topological recursion of Chekhov, Eynard and Orantin. By introducing two families of correlation functions, one corresponding to the meromorphic differentials $\omega_{g,n}$ of topological recursion, we obtain Dyson-Schwinger equations that eventually lead to the abstract loop equations being, together with their pole structure, the necessary condition for topological recursion. This strategy to show the exact solvability of the LSZ model establishes another approach towards the exceptional property of integrability in some quantum field theories. We compare differences in the loop equations for the LSZ model (with complex fields) and the Grosse-Wulkenhaar model (with hermitian fieldss) and their consequences for the resulting particular type of topological recursion that governs the models.