From scalar fields on quantum spaces to blobbed topological recursion

Abstract

We review the construction of the $\lambda {\varphi }^4$-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.

arXiv comment33 pages, 9 figures. Contribution to "Noncommutativity in Physics" (special volume initiated by CORFU2021)

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Cited by in corpus (10)

• From Noncommutative Geometry to Random Matrix Theory
• A Laplacian to compute intersection numbers on ${\bar{\mathcal{M}}}_{g,n}$ and correlation functions in NCQFT
• Complete solution of the LSZ Model via Topological Recursion
• Approximate treatment of noncommutative curvature in quartic matrix model
• $x-y$ duality in Topological Recursion for exponential variables via Quantum Dilogarithm
• The Tensor Track VII: From Quantum Gravity to Artificial Intelligence
• Blobbed topological recursion from extended loop equations
• The loop equations for noncommutative geometries on quivers
• Exact Solutions v.s. Perturbative Calculations of Finite ${\Phi }^3$-${\Phi }^4$ Hybrid-Matrix-Model
• Genus one free energy contribution to the quartic Kontsevich model