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The Classification of Non-Local Chiral CFT with c < 1

Abstract

All non-local but relatively local irreducible extensions of Virasoro chiral CFTs with c < 1 are classified. The classification, which is a prerequisite for the classification of local c < 1 boundary CFTs on a two-dimensional half-space, turns out to be 1 to 1 with certain pairs of A-D-E graphs with distinguished vertices.

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Correspondence to Roberto Longo.

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Dedicated to Hans-Jürgen Borchers on the occasion of his 80th birthday

Supported in part by JSPS.

Supported in part by EU network “Quantum Spaces - Noncommutative Geometry” HPRN-CT-2002-00280.

Supported in part by GNAMPA and MIUR.

Communicated by A. Connes

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Kawahigashi, Y., Longo, R., Pennig, U. et al. The Classification of Non-Local Chiral CFT with c < 1. Commun. Math. Phys. 271, 375–385 (2007). https://doi.org/10.1007/s00220-007-0199-1

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Keywords

  • Dynkin Diagram
  • Tensor Category
  • Bratteli Diagram
  • Coxeter Number
  • Irreducible Decomposition