caa a22 4500 467911541 CHVBK 20180406152850.0 cr unu---uuuuu 170328e20060601xx s 000 0 eng 10.1007/s11232-006-0075-8 doi (NATIONALLICENCE)springer-10.1007/s11232-006-0075-8 Integrals over moduli spaces, ground ring, and four-point function in minimal Liouville gravity [Elektronische Daten] [A. Belavin, Al. Zamolodchikov] Directly evaluating the correlation functions in 2D minimal gravity requires integrating over the moduli space. For degenerate fields, the higher equations of motion of the Liouville field theory allow converting the integrand to a derivative, which reduces the integral to boundary terms and the so-called curvature contribution. The latter is directly related to the vacuum expectation value of the corresponding ground-ring element. The action of this element on the cohomology related to a generic matter primary field is evaluated directly in terms of the operator product expansions of the degenerate fields. This allows constructing the ground-ring algebra and evaluating the curvature term in the four-point function. We also analyze the operator product expansions of the Liouville "logarithmic primaries” and calculate the relevant logarithmic terms. Based on this, we obtain an explicit expression for the four-point correlation number of one degenerate and three generic matter fields. We compare this integral with the numbers obtained from the matrix models of 2D gravity and discuss some related problems and ambiguities. Springer Science+Business Media, Inc., 2006 Polyakov string theory nationallicence Liouville gravity nationallicence Belavin A. Landau Institute for Theoretical Physics, RAS, Chernogolovka, Moscow Oblast, Russia aut Zamolodchikov Al Laboratoire de Physique Théorique et Astroparticules, Université Montpellier II, Montpellier, France aut Theoretical and Mathematical Physics Kluwer Academic Publishers-Consultants Bureau 147/3(2006-06-01), 729-754 0040-5779 147:3<729 2006 147 11232 https://doi.org/10.1007/s11232-006-0075-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11232-006-0075-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Belavin A. Landau Institute for Theoretical Physics, RAS, Chernogolovka, Moscow Oblast, Russia aut NATIONALLICENCE 700 1- Zamolodchikov Al Laboratoire de Physique Théorique et Astroparticules, Université Montpellier II, Montpellier, France aut NATIONALLICENCE 773 0- Theoretical and Mathematical Physics Kluwer Academic Publishers-Consultants Bureau 147/3(2006-06-01), 729-754 0040-5779 147:3<729 2006 147 11232 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer