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Communications in Mathematical Physics

, Volume 317, Issue 2, pp 425–445 | Cite as

C 2-Cofiniteness of 2-Cyclic Permutation Orbifold Models

  • Toshiyuki AbeEmail author
Article

Abstract

In this article, we consider permutation orbifold models of C 2-cofinite vertex operator algebras of CFT type. We show the C 2-cofiniteness of the 2-cyclic permutation orbifold model \({(V \otimes V)^{S_2} }\) for an arbitrary C 2-cofinite simple vertex operator algebra V of CFT type. We also give a proof of the C 2-cofiniteness of a \({\mathbb{Z}_{2}}\) -orbifold model \({V_{L}^{+}}\) of the lattice vertex operator algebra V L associated with a rank one positive definite even lattice L by using our result and the C 2-cofiniteness of V L .

Keywords

Vertex Operator Operator Algebra Vertex Operator Algebra Vertex Algebra Poisson Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. A.
    Abe T.: C 2-cofiniteness of the 2-cycle permutation orbifold models of minimal Virasoro vertex operator algebras. Commun. Math. Phys. 303, 825–844 (2011)ADSzbMATHCrossRefGoogle Scholar
  2. ABD.
    Abe T., Buhl G., Dong C.: Rationality, Regularity, and C 2-cofiniteness. Trans. Amer. Math. Soc. 356(8), 3391–3402 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  3. Ban1.
    Bantay P.: Characters and modular properties of permutation orbifolds. Phys. Lett. B419, 175–178 (1998)MathSciNetADSGoogle Scholar
  4. Ban02.
    Bantay P.: Permutation orbifolds. Nucl. Phys. B633(3), 365–378 (2002)MathSciNetADSCrossRefGoogle Scholar
  5. Ban3.
    Bantay P.: The kernel of the modular representation and the Galois action in RCFT. Commun. Math. Phys. 233, 423–438 (2003)MathSciNetADSzbMATHGoogle Scholar
  6. BDM.
    Barron K., Dong C., Mason G.: Twisted Sectors for Tensor Product Vertex Operator Algebras Associated to Permutation Groups. Commun. Math. Phys. 227, 349–384 (2002)MathSciNetADSzbMATHCrossRefGoogle Scholar
  7. BHS.
    Borisov L., Halpern M.B., Schweigert C.: Systematic approach to cyclic orbifolds. Int. J. Mod. Phys. A13, 125–168 (1998)MathSciNetADSGoogle Scholar
  8. Dong.
    Dong C.: Vertex algebras associated with even lattices. J. Alg. 160, 245–265 (1993)CrossRefGoogle Scholar
  9. DLM.
    Dong, C., Li, H., Mason, G.: Vertex Lie algebras, vertex Poisson algebras and vertex algebras. Contemp. Math., 297, Providence, RI: Amer. Math. Soc., 2002, pp. 67–96Google Scholar
  10. FHL.
    Frenkel, I., Huang, Y.-Z., Lepowsky, J.: On axiomatic approaches to vertex operator algebras and modules, Mem. Amer. Math. Soc., 104, Providence, RI: Amer. Math. Soc., 1993Google Scholar
  11. FLM.
    Frenkel, I., Lepowsky, J., Meurman, A.: Vertex Operator Algebras and the Monster. Pure and Appl. Math. 134, Boston, MA: Academic Press, 1988Google Scholar
  12. FKS.
    Fuchs J., Klemm A., Schmidt M.G.: Orbifolds by cyclic permutations in Gepner type superstrings in the corresponding Calabi-Yau manifolds. Ann, Phys. 214, 221–257 (1992)MathSciNetADSzbMATHCrossRefGoogle Scholar
  13. GN.
    Gaberdiel M., Neitzke A.: Rationality, quasirationality and finite W-algebras. Commun. Math. Phys. 238(1–2), 305–331 (2003)MathSciNetADSzbMATHGoogle Scholar
  14. KS.
    Klemm A., Schmidt M.G.: Orbifolds by cyclic permutations of tensor product conformal field theories. Phys. Lett. B245, 53–58 (1990)MathSciNetADSGoogle Scholar
  15. MN.
    Matsuo, A., Nagatomo, K.: Axioms for a vertex algebra and the locality of quantum fields. MSJ Memoirs 4, Tokyo: Mathematical Society of Japan, 1999Google Scholar
  16. M1.
    Miyamoto M.: Modular invariance of vertex operator algebras satisfying C 2-cofiniteness. Duke Math. J. 122(1), 51–91 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  17. M2.
    Miyamoto, M.: Flatness and Semi-Rigidity of Vertex Operator Algebras. http://arXiv.org/abs/1104.4675v1 [math.OA], 2011
  18. Yam.
    Yamskulna G.: (C 2)-cofiniteness of the vertex operator algebra \({V_{L}^{+}}\) when L is a rank one lattice. Commun. Alg. 32, 927–954 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  19. Z.
    Zhu Y.-C.: Modular invariance of characters of vertex operator algebras. J. Amer. Math. Soc. 9, 237–302 (1996)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of Science and EngineeringEhime UniversityMatsuyamaJapan

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