Symplectic Fermions

We study two-dimensional conformal field theories generated from a ``symplectic fermion'' - a free two-component fermion field of spin one - and construct the maximal local supersymmetric conformal field theory generated from it. This theory has central charge c=-2 and provides the simplest example of a theory with logarithmic operators. Twisted states with respect to the global SL(2,C)-symmetry of the symplectic fermions are introduced and we describe in detail how one obtains a consistent set of twisted amplitudes. We study orbifold models with respect to finite subgroups of SL(2,C) and obtain their modular invariant partition functions. In the case of the cyclic orbifolds explicit expressions are given for all two-, three- and four-point functions of the fundamental fields. The C_2-orbifold is shown to be isomorphic to the bosonic local logarithmic conformal field theory of the triplet algebra encountered previously. We discuss the relation of the C_4-orbifold to critical dense polymers.

• Publication year

  2000

• Venue

  Unknown venue

• Publication date

  2000-03-03

• Fields of study

  Physics

• Identifiers
  DOI 10.1016/S0550-3213(00)00295-9arXiv hep-th/0003029
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

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• No concepts are published for this paper.

• Supersymmetry and String Theory

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• conformal invariance

  2000influential reference
• gl(N|N) Super-current algebras for disordered Dirac fermions in two dimensions

  1999cited by this paper
• LOGARITHMIC OPERATORS IN THE THEORY OF PLATEAU TRANSITION

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• Disordered Dirac fermions: Multifractality termination and logarithmic conformal field theories

  1998cited by this paper
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  1998cited by this paper
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  1998cited by this paper
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  1998cited by this paper
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  1997cited by this paper
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  1997cited by this paper
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  1996cited by this paper
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  1996cited by this paper
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  1996cited by this paper
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  1995influential reference
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  1995cited by this paper
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