Coulomb integrals in Liouville theory and Liouville gravity
V. A. Fateev+*, A. V. Litvinov+
+L.D.Landau Institute for Theoretical Physics RAS, 142432 Chernogolovka, Moscow reg. Russia
*Laboratoire de Physique Théorique et Astroparticules, UniversitéMontpelier II, Pl.E. Bataillon, 34095 Montpelier, France
PACS: 11.25.Hf
Abstract
We study four-point correlation function in Liouville field
theory. If one of the fields is degenerate, such a function is described in
terms of Coulomb integrals. We find some non-trivial relations on these
integrals, which can be used to obtain new exact results in conformal field
theory. In particular, we calculate four-point correlation function in
minimal quantum gravity. The result agrees with the results obtained recently
by different methods [10fat-Belavin:2005yj,10fat-Kostov:2005av].