Enumeration of chord diagrams via topological recursion and quantum curve techniques

Abstract

In this paper we consider the enumeration of orientable and non-orientable chord diagrams. We show that this enumeration is encoded in appropriate expectation values of the $\beta$-deformed Gaussian and RNA matrix models. We evaluate these expectation values by means of the $\beta$-deformed topological recursion, and - independently - using properties of quantum curves. We show that both these methods provide efficient and systematic algorithms for counting of chord diagrams with a given genus, number of backbones and number of chords.

31 pages, 7 figures

References in corpus (1)

• Super-quantum curves from super-eigenvalue models

Cited by in corpus (2)

• Partial chord diagrams and matrix models
• The boundary length and point spectrum enumeration of partial chord diagrams using cut and join recursion