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Mosc. Math. J., 2015, Volume 15, Number 2, Pages 269–282 (Mi mmj558)  

Minimal Liouville gravity from Douglas string equation

A. Belavinabc, V. Belavindb

a L. D. Landau Institute for Theoretical Physics, 142432 Chernogolovka, Russia
b Institute for Information Transmission Problems, 127994 Moscow, Russia
c Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Russia
d P. N. Lebedev Physical Institute, 119991 Moscow, Russia

Abstract: We describe the connection between Minimal Liouville gravity, Douglas string equation and Frobrenius manifolds. We show that the appropriate solution of the Douglas equation and a proper transformation from the KdV to the Liouville frames leads to the fulfilment of the selection rules of the underlying conformal field theory. We review the properties of Minimal Liouville gravity and Frobenius manifolds and show that the required solution of the string equation takes simple form in the flat coordinates on the Frobenious manifold in the case of unitary Minimal Liouville gravity.

Key words and phrases: string theory, conformal field theory, two-dimensional gravity, Frobenius manifolds, tau function, integrable models.

DOI: https://doi.org/10.17323/1609-4514-2015-15-2-269-282

Full text: http://www.mathjournals.org/.../2015-015-002-005.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 81, 16, 51
Received: June 12, 2014; in revised form November 17, 2014
Language:

Citation: A. Belavin, V. Belavin, “Minimal Liouville gravity from Douglas string equation”, Mosc. Math. J., 15:2 (2015), 269–282

Citation in format AMSBIB
\Bibitem{BelBel15}
\by A.~Belavin, V.~Belavin
\paper Minimal Liouville gravity from Douglas string equation
\jour Mosc. Math.~J.
\yr 2015
\vol 15
\issue 2
\pages 269--282
\mathnet{http://mi.mathnet.ru/mmj558}
\crossref{https://doi.org/10.17323/1609-4514-2015-15-2-269-282}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3427423}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000361607300005}


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