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Solitons in Affine and Permutation Orbifolds

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Abstract

We consider properties of solitons in general orbifolds in the algebraic quantum field theory framework and constructions of solitons in affine and permutation orbifolds. Under general conditions we show that our construction gives all the twisted representations of the fixed point subnet. This allows us to prove a number of conjectures: in the affine orbifold case we clarify the issue of “fixed point resolutions”; in the permutation orbifold case we determine all irreducible representations of the orbifold, and we also determine the fusion rules in a nontrivial case, which imply an integral property of chiral data for any completely rational conformal net.

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Authors and Affiliations

  1. Department of Mathematics, MIT, Cambridge, MA, 02139, USA

    Victor G. Kac

  2. Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 1, 00133, Roma, Italy

    Roberto Longo

  3. Department of Mathematics, University of California at Riverside, Riverside, CA, 92521, USA

    Feng Xu

Authors
  1. Victor G. Kac
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  2. Roberto Longo
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  3. Feng Xu
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Correspondence to Feng Xu.

Additional information

Communicated by Y. Kawahigashi

Supported in part by NSF.

Supported in part by GNAMPA-INDAM and MIUR.

Supported in part by NSF.

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Kac, V., Longo, R. & Xu, F. Solitons in Affine and Permutation Orbifolds. Commun. Math. Phys. 253, 723–764 (2005). https://doi.org/10.1007/s00220-004-1160-1

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