Abstract
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.
Highlights
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
Two-dimensional quantum gravity coupled to a free massless Majorana fermion field theory in the light-cone gauge had been studied in Ref. [4], where the non-integrated four-point correlation function of the gravitationally dressed operators, which has logarithmic behaviour, was obtained
We consider a certain class of four-point correlation functions of local Liouville operators, which can be regarded 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
Summary
Q, the operator eβφ(ξ) can be interpreted as a local operator. The cosmological term operator eαφ(ξ) in the action (1) is a particular case of the operator (9) with Φ1,1(ξ). We consider non-integrated four-point correlation functions of the gravitationally dressed operators on a sphere with fixed area A. In order to study general properties of the correlation functions, we use local operators eβiφ(ξ) with real βi which is not fixed by Eq (10). The correlation functions are separated into the Liouville part and the matter part as.
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