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TMF, 1992, Volume 93, Number 2, Pages 354–368 (Mi tmf1533)  

This article is cited in 1 scientific paper (total in 1 paper)

Multicut solutions of the matrix Kontsevich–Penner model

K. L. Zarembo, L. O. Chekhov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: Multicut solutions of the Hermitian one-matrix model parametrized by the recently introduced matrix model [1] with external field and Lagrangian having the form $ \operatorname {tr}{(\Lambda X\Lambda X)} - \alpha N$ $(\log {(1+X)} -X)$ are considered. A brief review of the model, which describes the discretized moduli space of Riemann surfaces, is given. The general structure of multicut solutions is investigated, and it is shown that there arises an additional symmetry and that $s$ parameters remain free for the $(s+1)$-cut solution. A detailed analysis of the one-cut solution is made. Among other results, all solutions of Kazakov type are reproduced. We also discuss the general form for the two-cut solution which arises as generalization of the string equation to the case of two cuts. The entire treatment is given in the approximation of planar diagrams.

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English version:
Theoretical and Mathematical Physics, 1992, 93:2, 1328–1336

Bibliographic databases:

Document Type: Article
Received: 17.06.1992

Citation: K. L. Zarembo, L. O. Chekhov, “Multicut solutions of the matrix Kontsevich–Penner model”, TMF, 93:2 (1992), 354–368; Theoret. and Math. Phys., 93:2 (1992), 1328–1336

Citation in format AMSBIB
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\by K.~L.~Zarembo, L.~O.~Chekhov
\paper Multicut solutions of the matrix Kontsevich--Penner model
\jour TMF
\yr 1992
\vol 93
\issue 2
\pages 354--368
\mathnet{http://mi.mathnet.ru/tmf1533}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1233551}
\zmath{https://zbmath.org/?q=an:0788.32016}
\transl
\jour Theoret. and Math. Phys.
\yr 1992
\vol 93
\issue 2
\pages 1328--1336
\crossref{https://doi.org/10.1007/BF01083530}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1992LJ23200012}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. L. O. Chekhov, “Matrix Models: Geometry of Moduli Spaces and Exact Solutions”, Theoret. and Math. Phys., 127:2 (2001), 557–618  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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