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Logarithmic Conformal Field Theories via Logarithmic Deformations

J. Fjelstad·J. Fuchs·S. Hwang·A. M. Semikhatov·I. Yu. Tipunin
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Abstract

We construct logarithmic conformal field theories starting from an ordinary conformal field theory -- with a chiral algebra C and the corresponding space of states V -- via a two-step construction: i) deforming the chiral algebra representation on V\tensor End K[[z,1/z]], where K is an auxiliary finite-dimensional vector space, and ii) extending C by operators corresponding to the endomorphisms End K. For K=C^2, with End K being the two-dimensional Clifford algebra, our construction results in extending C by an operator that can be thought of as \partial^{-1}E, where \oint E is a fermionic screening. This covers the (2,p) Virasoro minimal models as well as the sl(2) WZW theory.

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J. Fjelstad, J. Fuchs, S. Hwang, A. M. Semikhatov, I. Yu. Tipunin. 2002-01-22. Logarithmic Conformal Field Theories via Logarithmic Deformations. https://doi.org/10.1016/s0550-3213(02)00220-1

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