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

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• 作者：J?rgen E. Andersen ; Leonid O. Chekhov ; R.C. Penner ; Christian M. Reidys ; Piotr Su?kowski
• 关键词：Chord diagrams ; Matrix model ; Riemann?s moduli space ; RNA ; Topological recursion
• 刊名：Nuclear Physics B
• 出版年：2013
• 出版时间：21 January, 2013
• 年：2013
• 卷：866
• 期：3
• 页码：414-443
• 全文大小：406 K

文摘

We introduce and study the Hermitian matrix model with potential , 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 . 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.