Nested Catalan tables and a recurrence relation in noncommutative quantum field theory
Mathematical Physics
2022-04-15 v2 Combinatorics
math.MP
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.
Cite
@article{arxiv.1904.11231,
title = {Nested Catalan tables and a recurrence relation in noncommutative quantum field theory},
author = {Jins de Jong and Alexander Hock and Raimar Wulkenhaar},
journal= {arXiv preprint arXiv:1904.11231},
year = {2022}
}
Comments
24 pages, 17 figures. v2 implements several improvements suggested by an anonymous referee