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

Jørgen Ellegaard Andersen, Leonid chekhov, Robert Penner, Christian Reidys, Piotr Sułkowski

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Abstract

We introduce and study the Hermitian matrix model with potential V s,t(x)=x 2/2-stx/(1-tx), which enumerates the number of linear chord diagrams with no isolated vertices 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 in genus less than four.

Original languageEnglish
JournalNuclear Physics B
Volume866
Issue number3
Pages (from-to)414-443
ISSN1873-1562
DOIs
Publication statusPublished - 2013

Keywords

  • hep-th
  • math-ph
  • math.AG
  • math.GT
  • math.MP
  • q-bio.QM
  • Topological recursion
  • RNA
  • Riemann's moduli space
  • Matrix model
  • Chord diagrams

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