We obtain logarithmic behaviours of a four-point correlation function in the c = −2 conformal field theory by using the Feigin-Fuchs construction. It becomes an indeterminate form by a naive evaluation, but is obtained by introducing an appropriate regularization procedure. *
We study four-point correlation functions with logarithmic behaviour in Liouville field theory on a sphere, which consist of one kind of the local operators. We study them as non-integrated correlation functions of the gravitational sector of two-dimensional quantum gravity coupled to an ordinary conformal field theory in the conformal gauge. We also examine, in the (p, q) minimal conformal field theories, a condition of the appearance of logarithmic correlation functions of gravitationally dressed operators. *
We study the simplest examples of minimal string theory whose worldsheet description is the unitary (p, q) minimal model coupled to twodimensional gravity (Liouville field theory). In the Liouville sector, we show that four-point correlation functions of 'tachyons' exhibit logarithmic singularities, and that the theory turns out to be logarithmic. The relation with Zamolodchikov's logarithmic degenerate fields is also discussed. Our result holds for generic values of (p, q).
We study a two-dimensional conformal field theory coupled to quantum gravity on a disk. Using the continuum Liouville field approach, we compute three-point correlation functions of boundary operators. The structure of momentum singularities is different from that of correlation functions on a sphere and is more complicated. We also compute four-point functions of boundary operators and three-point functions of two boundary operators and one bulk operator.
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