Three-point functions and operator product expansion in the SL(2) conformal field theory
نویسنده
چکیده
In the SL(2) conformal field theory, we write down and analyze the analytic expression of the three-point functions of generic primary fields with definite SL(2) weights. Using these results, we discuss the operator product expansion in the SL(2, R) WZW model. We propose a prescription of the OPE, the classical limit of which is in precise agreement with the tensor products of the representations of SL(2, R).
منابع مشابه
Operator product expansion in SL(2) conformal field theory
In the conformal field theories having affine SL(2) symmetry, we study the operator product expansion (OPE) involving primary fields in highest weight representations. For this purpose, we analyze properties of primary fields with definite SL(2) weights, and calculate their twoand three-point functions. Using these correlators, we show that the correct OPE is obtained when one of the primary fi...
متن کاملar X iv : h ep - t h / 01 07 24 2 v 1 2 7 Ju l 2 00 1 Operator Product Expansion in Logarithmic Conformal Field Theory
In logarithmic conformal field theory, primary fields come together with logarithmic partner fields on which the stress-energy tensor acts non-diagonally. Exploiting this fact and global conformal invariance of two-and three-point functions, operator product expansions of logarithmic operators in arbitrary rank logarithmic conformal field theory are derived.
متن کاملOperator product expansion in the SL 2 conformal field theory
We discuss the operator product expansion (OPE) in the models with the SL2 affine symmetry. For this purpose, we calculate the correlation functions of the primary fields with definite SL2 weights. By using them and extending the arguments in the literature, we show that the OPE with one primary field in a degenerate representation is correctly obtained. We also study the OPE among the primary ...
متن کاملThe 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 ord...
متن کاملOperator Product Expansion in Logarithmic Conformal Field Theory
In logarithmic conformal field theory, primary fields come together with logarithmic partner fields on which the stress-energy tensor acts non-diagonally. Exploiting this fact and global conformal invariance of twoand three-point functions, operator product expansions of logarithmic operators in arbitrary rank logarithmic conformal field theory are investigated. Since the precise relationship b...
متن کامل