The Logarithmic Conformal Field Theories

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 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. 1 Introduction It has been shown by Gurarie [1], that in the OPE of two given local fields which has at least two fields with the same conformal dimension, one may find some operators with a special property, know..