Topological recursion for chord diagrams, RNA complexes, and cells in moduli spaces
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 Riemannʼs moduli spaces for bordered surfaces. The free energies are computed here in principle for all genera and explicitly in genus less than four.
Additional Information
© 2012 Elsevier B. V. Received 23 May 2012; accepted 17 September 2012; Available online 20 September 2012. JEA and RCP are supported by the Centre for Quantum Geometry of Moduli Spaces which is funded by the Danish National Research Foundation. The research of LCh is supported by the Russian Foundation for Basic Research (Grants Nos. 10-02-01315-a, 11-01-12037-ofi-m-2011, and 11-02-90453-Ukr-f-a) by the Program Mathematical Methods of Nonlinear Dynamics and by the Grant of Supporting Leading Scientific Schools NSh-4612.2012.1. The research of PS is supported by the DOE grant DE-FG03-92-ER40701FG-02, the European Commission under the Marie-Curie International Outgoing Fellowship Programme, and the Foundation for Polish Science. RCP also acknowledges the kind support of Institut Henri Poincaré where parts of this manuscript were written.Additional details
- Eprint ID
- 35643
- DOI
- 10.1016/j.nuclphysb.2012.09.012
- Resolver ID
- CaltechAUTHORS:20121126-134532713
- Danish National Research Foundation Centre for Quantum Geometry of Moduli Spaces
- 10-02-01315-a
- Russian Foundation for Basic Research
- 11-01-12037-ofi-m-2011
- Russian Foundation for Basic Research
- 11-02-90453-Ukr-f-a
- Russian Foundation for Basic Research
- Program Mathematical Methods of Nonlinear Dynamics
- NSh-4612.2012.1
- Grant of Supporting Leading Scientific Schools
- DE-FG03-92-ER40701FG-02
- Department of Energy (DOE)
- Marie-Curie International Outgoing Fellowship Programme European Commission
- Foundation for Polish Science
- Institut Henri Poincaré
- Created
-
2012-11-26Created from EPrint's datestamp field
- Updated
-
2021-11-09Created from EPrint's last_modified field