Operator Product Coefficients in Non-Diagonal Conformal Field Theories

摘要

The problems involved in the determination of operator product coefficients in nondiagonal conformal field theories (RCFTs) are explained. The methods of Dotsenko and Fateev are used to derive formulae which allow computing these coefficients. A careful treatment of the issue of uniqueness of the results proves to be necessary. It is deemed appropriate to analyze the four-point functions of RCFTs in sufficient detail so as to be able to determine unambiguously the operator product coefficients of these theories. The outcome of such an analysis is examined (details will appear elsewhere). It turns out that the methods of Dotsenko and Fateev are sufficient to attack the nondiagonal case, provided the subtle issue of uniqueness of the four-point functions is taken care of. The formulae are somewhat unwieldy, but can be easily evaluated on a computer. The results apply directly to the case of c<1 RCFTs and to A1 Wess-Zumino-Witten theories where the differential equations for the four-point functions are known explicitly, but analogous considerations will be valid for any RCFT.