Nested Catalan tables and a recurrence relation in noncommutative quantum field theory
Jins de Jong, Alexander Hock, Raimar Wulkenhaar (M\"unster)
TL;DR
This paper introduces nested Catalan tables, a new combinatorial structure linked to correlation functions in noncommutative quantum field theory, providing explicit solutions to recurrence relations via Catalan numbers.
Contribution
It presents the first explicit solution to a recurrence relation in quantum field theory using nested Catalan tables, connecting combinatorics with physics.
Findings
Explicit solution to the recurrence relation
Nested Catalan tables counted by Catalan numbers
Diagrammatic representation as non-crossing chords and threads
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.
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