Complete solution of the LSZ Model via Topological Recursion

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.

arXiv comment63 pages, 6 figures

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Cited by in corpus (5)

• Solution of all quartic matrix models
• On the $x$-$y$ Symmetry of Correlators in Topological Recursion via Loop Insertion Operator
• A Laplacian to compute intersection numbers on ${\bar{\mathcal{M}}}_{g,n}$ and correlation functions in NCQFT
• $x-y$ duality in Topological Recursion for exponential variables via Quantum Dilogarithm
• Blobbed topological recursion from extended loop equations