Topological recursion for chord diagrams, RNA complexes, and cells in moduli spaces

Abstract

We introduce and study the Hermitian matrix model with potential V(x)=x^2/2-stx/(1-tx), which enumerates the number of linear chord diagrams of fixed genus with specified numbers of backbones generated by s and chords generated by t. For the one-cut solution, the partition function, correlators and free energies are convergent for small t and all s as a perturbation of the Gaussian potential, which arises for st=0. This perturbation is computed using the formalism of the topological recursion. The corresponding enumeration of chord diagrams gives at once the number of RNA complexes of a given topology as well as the number of cells in Riemann's moduli spaces for bordered surfaces. The free energies are computed here in principle for all genera and explicitly for genera less than four.

34 pages, 2 figures

References in corpus (6)

• Remodeling the B-model
• Les Houches lectures on matrix models and topological strings
• A-polynomial, B-model, and Quantization
• From Brezin-Hikami to Harer-Zagier formulas for Gaussian correlators
• Thermodynamics of a model for RNA folding
• On a proof of the Bouchard-Sulkowski conjecture

Cited by in corpus (14)

• Quantum curves and conformal field theory
• Models of discretized moduli spaces, cohomological field theories, and Gaussian means
• Enumeration of RNA complexes via random matrix theory
• Enumeration of chord diagrams on many intervals and their non-orientable analogs
• Enumeration of meanders and Masur-Veech volumes
• Strands algebras and Ozsváth-Szabó's Kauffman-states functor
• Computing the spectral action for fuzzy geometries: from random noncommutative geometry to bi-tracial multimatrix models
• Partial chord diagrams and matrix models
• Comment on "The phase diagram of the multi-matrix model with ABAB-interaction from functional renormalization"
• RNA substructure as a random matrix ensemble
• Graph calculus and the disconnected-boundary Schwinger-Dyson equations of quartic tensor field theories
• Trivalent vertices and bordered knot Floer homology in the standard basis
• Genus Comparisons in the Topological Analysis of RNA Structures
• The boundary length and point spectrum enumeration of partial chord diagrams using cut and join recursion