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Moduli integrals and ground ring in minimal liouville gravity
A. A. Belavin, A. B. Zamolodchikov*
L. D. Landau Institute for Theoretical Physics RAS, 142432 Chernogolovka, Moscov reg., Russia
*Laboratoire de Physique Théorique et Astroparticules, Université Montpelier II, Pl.E. Bataillon, 34095 Montpelier, France

PACS: 11.25.Hf
Straightforward evaluation of the correlation functions in 2D minimal gravity requires integration over the moduli space. For degenerate fields the Liouville higher equations of motion allow to turn the integrand to a derivative and thus to reduce it to the boundary terms plus so-called curvature contribution. The last is directly related to the expectation value of the corresponding ground ring element. We use the operator product expansion technique to reproduce the ground ring construction explicitly in terms of the (generalized) minimal matter and Liouville degenerate fields. The action of the ground ring on the generic primary fields is evaluated explicitly. This permits us to construct directly the ground ring algebra. Detailed analysis of the ground ring mechanism is helpful in the understanding of the boundary terms and their evaluation.

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