Nested Catalan tables and a recurrence relation in noncommutative quantum field theory

Abstract

Correlation functions in a dynamic quartic matrix model are obtained from the two-point function through a recurrence relation. This paper gives the explicit solution of the recurrence by mapping it bijectively to a two-fold nested combinatorial structure each counted by Catalan numbers. These `nested Catalan tables' have a description as diagrams of non-crossing chords and threads.

24 pages, 17 figures. v2 implements several improvements suggested by an anonymous referee

References in corpus (4)

• Progress in solving a noncommutative quantum field theory in four dimensions
• Blobbed topological recursion of the quartic Kontsevich model I: Loop equations and conjectures
• Solution of all quartic matrix models
• Perturbative and Geometric Analysis of the Quartic Kontsevich Model

Cited by in corpus (5)

• Blobbed topological recursion of the quartic Kontsevich model I: Loop equations and conjectures
• Solution of all quartic matrix models
• From scalar fields on quantum spaces to blobbed topological recursion
• 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