Logarithmic Operators in Conformal Field Theory and The $\W_\infty$-algebra

Abstract

It is shown explicitly that the correlation functions of Conformal Field Theories (CFT) with the logarithmic operators are invariant under the differential realization of Borel subalgebra of $\W_\infty$-algebra. This algebra is constructed by tensor-operator algebra of differential representation of ordinary $sl(2,C)$. This method allows us to write differential equations which can be used to find general expression for three and four-point correlation functions possessing logarithmic operators. The operator product expansion (OPE) coefficients of general logarithmic CFT are given up to third level.

19 pages, LaTex, no figures, Version to appear in Int. J. Mod. Phys. A 12 (1997)

References in corpus (12)

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• A Local Logarithmic Conformal Field Theory
• An algebraic approach to logarithmic conformal field theory
• Matrix D-brane Dynamics, Logarithmic Operators and Quantization of Noncommutative Spacetime
• D-Brane Recoil Mislays Information
• 2-Dimensional Turbulence: yet another Conformal Field Theory Solution
• Singular Vectors in Logarithmic Conformal Field Theories
• A Logarithmic Conformal Field Theory Solution For Two Dimensional Magnetohydrodynamics In Presence of The Alf'ven Effect
• Logarithmic Conformal Field Theory and Seiberg-Witten Models
• Disordered Systems and Logarithmic Conformal Field Theory
• Gradient Flow in Logarithmic Conformal Field Theory
• Logarithmic conformal field theories with continuous weights
• Legendre's Relation and the Quantum Equivalence osp(4|4)_(1) = osp(2|2)_(-2) + su(2)_(0)
• Zamalodchikov's C-Theorem and The Logarithmic Conformal Field Theory
• Quenched Averaged Correlation Functions of the Random Magnets
• The O(n) Model in the $n\to 0$ Limit (self-avoiding-walks) and Logarithmic Conformal Field Theory
• Logarithmic Correlation Functions in Liouville Field Theory
• Minimal String Theory is Logarithmic