Null Vectors in Logarithmic Conformal Field Theory

Abstract

The representation theory of the Virasoro algebra in the case of a logarithmic conformal field theory is considered. Here, indecomposable representations have to be taken into account, which has many interesting consequences. We study the generalization of null vectors towards the case of indecomposable representation modules and, in particular, how such logarithmic null vectors can be used to derive differential equations for correlation functions. We show that differential equations for correlation functions with logarithmic fields become inhomogeneous.

7 pages, LaTeX2e, Invited talk at the TMR conference ``Non-perturbative quantum effects 2000'', Paris, September 2000

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• Operator Product Expansion in Logarithmic Conformal Field Theory
• Jordan cells in logarithmic limits of conformal field theory
• Affine Jordan cells, logarithmic correlators, and hamiltonian reduction
• On logarithmic solutions to the conformal Ward identities
• Notes on Generalised Nullvectors in logarithmic CFT
• Extended chiral algebras and the emergence of SU(2) quantum numbers in the Coulomb gas
• Operator Algebra in Logarithmic Conformal Field Theory
• Logarithmic operators in $c=0$ bulk CFTs
• Contour Integral Representations for the Characters of Logarithmic CFTs