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arxiv: hep-th/9510149 · v1 · submitted 1995-10-20 · ✦ hep-th

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Curiosities at c=-2

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classification ✦ hep-th
keywords conformalconstructionlogarithmicmodelsoperatorstermstheoryalgebra
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Conformal field theory at $c=-2$ provides the simplest example of a theory with ``logarithmic'' operators. We examine in detail the $(\xi,\eta)$ ghost system and Coulomb gas construction at $c=-2$ and show that, in contradistinction to minimal models, they can not be described in terms of conformal families of {\em primary\/} fields alone but necessarily contain reducible but indecomposable representations of the Virasoro algebra. We then present a construction of ``logarithmic'' operators in terms of ``symplectic'' fermions displaying a global $SL(2)$ symmetry. Orbifolds with respect to finite subgroups of $SL(2)$ are reminiscent of the $ADE$ classification of $c=1$ modular invariant partition functions, but are isolated models and not linked by massless flows.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Non-Hermitian free-fermion critical systems and logarithmic conformal field theory

    cond-mat.str-el 2026-02 unverdicted novelty 7.0

    A PT-symmetric non-Hermitian free-fermion field theory realizes logarithmic conformal field theory with central charge c=-2 via a biorthogonal Virasoro algebra construction.