The Logarithmic Conformal Field Theories

Abstract

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 operator product expansion (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.

17 pages ,latex , some minor changes, to appear in Nucl. Phys. B

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• Logarithmic Conformal Field Theory Through Nilpotent Conformal Dimensions
• Short-cut to new anomalies in gravity duals to logarithmic conformal field theories
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• Logarithmic Operators in Conformal Field Theory and The $\W_\infty$-algebra
• The Neveu-Schwarz and Ramond Algebras of Logarithmic Superconformal Field Theory
• SU(2)_0 and OSp(2|2)_{-2} WZNW models : Two current algebras, one Logarithmic CFT
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• Disordered Systems and Logarithmic Conformal Field Theory
• Dynamical symmetries and causality in non-equilibrium phase transitions
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• Prelogarithmic operators and Jordan blocks in SL(2)_k affine algebra
• Logarithmic conformal field theories with continuous weights
• Jordan cells in logarithmic limits of conformal field theory
• Use of Nilpotent weights in Logarithmic Conformal Field Theories
• Legendre's Relation and the Quantum Equivalence osp(4|4)_(1) = osp(2|2)_(-2) + su(2)_(0)
• Logarithmic Currents in the SU(2)_0 WZNW model
• Zamalodchikov's C-Theorem and The Logarithmic Conformal Field Theory
• Quenched Averaged Correlation Functions of the Random Magnets
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• Note on SLE and logarithmic CFT
• Causality from dynamical symmetry: an example from local scale-invariance
• Logarithmic Primary Fields in Conformal and Superconformal Field Theory
• Logarithmic Conformal Field Theories and Strings in Changing Backgrounds
• Extended chiral algebras in the SU(2)_0 WZNW model
• A mass hierarchy from recoiling D branes
• Physical ageing and new representations of some Lie algebras of local scale-invariance
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• On logarithmic solutions to the conformal Ward identities
• The O(n) Model in the $n\to 0$ Limit (self-avoiding-walks) and Logarithmic Conformal Field Theory
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• Towards the Construction of Local Logarithmic Conformal Field Theories
• Extended multiplet structure in Logarithmic Conformal Field Theories
• Logarithmic Correlation Functions in Liouville Field Theory
• On conformal Jordan cells of finite and infinite rank
• Quantizing field theories in noncommutative geometry and the correspondence between anti de Sitter space and conformal field theory
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• Stress Energy tensor in LCFT and the Logarithmic Sugawara construction
• Minimal String Theory is Logarithmic
• A Novel Mass Hierarchy and Discrete Excitation Spectra from Quantum-Fluctuating D-branes
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• Correlation Functions in N=3 Superconformal Theory
• Relativistic conformal symmetry of neural field propagation in the brain
• Implications of Space-Time foam for Entanglement Correlations of Neutral Kaons
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