THE LOGARITHMIC CONFORMAL FIELD-THEORIES

We study the correlation functions of logarithmic conformal field theo ries, First, assuming conformal invariance, we explicitly calculate tw o- 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 logar ithmic field as a formal derivative of the ordinary field with respect to its conformal weight. This enables one to calculate any a-point fu nction containing the logarithmic held in terms of ordinary n-point fu nctions, Finally, we calculate the operator product expansion (OPE) co efficients of a logarithmic conformal field theory, and show that thes e can be obtained from the corresponding coefficients of ordinary conf ormal theory by a simple derivation. (C) 1997 Elsevier Science B.V.