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Topological recursion for Gaussian means and cohomological field theories

Andersen, Jørgen Ellegaard and Chekhov, Leonid O. and Norbury, Paul and Penner, Robert C. (2015) Topological recursion for Gaussian means and cohomological field theories. Theoretical and Mathematical Physics, 185 (3). pp. 1685-1717. ISSN 0040-5779. https://resolver.caltech.edu/CaltechAUTHORS:20160205-094746432

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Abstract

We introduce explicit relations between genus-filtrated s-loop means of the Gaussian matrix model and terms of the genus expansion of the Kontsevich–Penner matrix model (KPMM), which is the generating function for volumes of discretized (open) moduli spaces M_(g,s)^(disc) (discrete volumes). Using these relations, we express Gaussian means in all orders of the genus expansion as polynomials in special times weighted by ancestor invariants of an underlying cohomological field theory. We translate the topological recursion of the Gaussian model into recurrence relations for the coefficients of this expansion, which allows proving that they are integers and positive. We find the coefficients in the first subleading order for M_(g,1) for all g in three ways: using the refined Harer–Zagier recursion, using the Givental-type decomposition of the KPMM, and counting diagrams explicitly.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/s11232-015-0373-0DOIArticle
http://link.springer.com/article/10.1007/s11232-015-0373-0PublisherArticle
http://arxiv.org/abs/1512.09309arXivDiscussion Paper
Additional Information:© 2015 Pleiades Publishing. Sections 2, 3, and 6.2 were written by L. O. Chekhov, and Secs. 1, 4, 5, and 7 and also the other parts of Sec. 6 were written by J. E. Andersen, P. Norbury, and R. C. Penner. The research of L. O. Chekhov was funded by a grant from the Russian Science Foundation (Project No. 14-50-00005) and was performed in Steklov Mathematical Institute of Russian Academy of Sciences. Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 185, No. 3, pp. 371–409, December, 2015.
Funders:
Funding AgencyGrant Number
Russian Science Foundation14-50-00005
Subject Keywords:chord diagram; Givental decomposition; Kontsevich–Penner matrix model; discrete volume; moduli space; Deligne–Mumford compactification
Issue or Number:3
Record Number:CaltechAUTHORS:20160205-094746432
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160205-094746432
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:64265
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:08 Feb 2016 19:03
Last Modified:03 Oct 2019 09:36

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