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Moscow Mathematical Journal

Volume 15, Issue 2, April–June 2015  pp. 269–282.

Minimal Liouville Gravity from Douglas String Equation

Authors:  A. Belavin (1) and V. Belavin (2)
Author institution:(1) L. D. Landau Institute for Theoretical Physics, 142432 Chernogolovka, Russia, Institute for Information Transmission Problems, 127994 Moscow, Russia, and Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Russia
(2) P. N. Lebedev Physical Institute, 119991 Moscow, Russia, and Institute for Information Transmission Problems, 127994 Moscow, Russia


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.

2010 Math. Subj. Class. 81, 16, 51.

Keywords: String theory, conformal field theory, two-dimensional gravity, Frobenius manifolds, tau function, integrable models.

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