Logarithmic Conformal Field Theory Through Nilpotent Conformal Dimensions

Abstract

We study logarithmic conformal field theories (LCFTs) through the introduction of nilpotent conformal weights. Using this device, we derive the properties of LCFT's such as the transformation laws, singular vectors and the structure of correlation functions. We discuss the emergence of an extra energy momentum tensor, which is the logarithmic partner of the energy momentum tensor.

17 pages, Latex

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• Holographic Rényi entropy in AdS${}_3$/LCFT${}_2$ correspondence
• The Neveu-Schwarz and Ramond Algebras of Logarithmic Superconformal Field Theory
• Notes on non-trivial and logarithmic CFTs with c=0
• On logarithmic extensions of local scale-invariance
• Logarithmic Correlators in Non-relativistic Conformal Field Theory
• On the AdS/CFT Correspondence and Logarithmic Operator
• Use of Nilpotent weights in Logarithmic Conformal Field Theories
• Proposal for a CFT interpretation of Watts' differential equation for percolation
• Affine Jordan cells, logarithmic correlators, and hamiltonian reduction
• On Holographic Realization of Logarithmic GCA
• Note on SLE and logarithmic CFT
• Some Properties of Sandpile Models as Prototype of Self-Organized Critical Systems
• Logarithmic Conformal Null Vectors and SLE
• Logarithmic Exotic Conformal Galilean Algebras
• Calculation of Four Point Correlation Function of Logarithmic Conformal Field Theory Using AdS/CFT Correspondence
• Logarithmic correlators or responses in non-relativistic analogues of conformal invariance
• Notes on Generalised Nullvectors in logarithmic CFT
• Four-Point Functions in Logarithmic Conformal Field Theories
• On logarithmic solutions to the conformal Ward identities
• Correlation Functions and AdS/LCFT Correspondence
• Stress Energy tensor in LCFT and the Logarithmic Sugawara construction
• Perturbed Logarithmic CFT and Integrable Models
• SLE($\kappa ,\rho$)and Boundary Coulomb Gas