The Logarithmic Conformal Field Theories

Abstract

We study the correlation functions of logarithmic conformal field theories. First, assuming conformal invariance, we explicitly calculate two-- and three-- point functions. This calculation is done for the general case of more than one logarithmic field in a block, and more than one set of logarithmic fields. Then we show that one can regard the logarithmic field as a formal derivative of the ordinary field with respect to its conformal weight. This enables one to calculate any $n$-- point function containing the logarithmic field in terms of ordinary $n$--point functions. At last, we calculate the operator product expansion (OPE) coefficients of a logarithmic conformal field theory, and show that these can be obtained from the corresponding coefficients of ordinary conformal theory by a simple derivation.