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.

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

References in corpus (7)

• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• Two and Three Loops Beta Function of Non Commutative ${\Phi }_4^4$ Theory
• Progress in solving a noncommutative quantum field theory in four dimensions
• Renormalization in combinatorially non-local field theories: the Hopf algebra of 2-graphs
• Matrix Field Theory
• Renormalization in Combinatorially Non-Local Field Theories: the BPHZ Momentum Scheme
• Blobbed topological recursion for correlation functions in tensor models

Cited by in corpus (9)

• From Noncommutative Geometry to Random Matrix Theory
• Approximate treatment of noncommutative curvature in quartic matrix model
• Complete solution of the LSZ Model via Topological Recursion
• $x-y$ 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
• Genus one free energy contribution to the quartic Kontsevich model
• Exact Solutions v.s. Perturbative Calculations of Finite ${\Phi }^3$-${\Phi }^4$ Hybrid-Matrix-Model
• The loop equations for noncommutative geometries on quivers