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Curiosities at c=-2

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arxiv hep-th/9510149 v1 pith:X4F2FNOZ submitted 1995-10-20 hep-th

Horst G. Kausch This is my paper · ORCID
classification hep-th
keywords conformalconstructionlogarithmicmodelsoperatorstermstheoryalgebra
verification ladder T0 review T1 audit T2 compute T3 formal

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abstract

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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Cited by 3 Pith papers

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

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

    cond-mat.str-el 2026-02 unverdicted novelty 7.0 of 10

    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.

  2. Logarithmic correlation functions for critical dense polymers on the cylinder

    cond-mat.stat-mech 2019-07 unverdicted novelty 7.0 of 10

    Explicit finite-n lattice correlators for dense polymers on a cylinder are computed via Temperley-Lieb algebra and shown to match ratios of c=-2 CFT correlators involving boundary fields of dimensions -1/8 and 0, with...

  3. Entanglement spectrum and entropy in topological non-Hermitian systems and non-unitary conformal field theories

    cond-mat.str-el 2019-09 conditional novelty 6.0 of 10

    At a critical point of a PT-symmetric non-Hermitian SSH chain, the biorthogonal entanglement entropy scales logarithmically with central charge c=-2, attributed to a bc-ghost non-unitary CFT.

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