Skip to main content
SpringerLink
Log in

Z/NZ Conformal Field Theories

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

We compute the modular properties of the possible genus-one characters of some Rational Conformal Field Theories starting from their fusion rules. We show that the possible choices ofS matrices are indexed by some automorphisms of the fusion algebra. We also classify the modular invariant partition functions of these theories. This gives the complete list of modular invariant partition functions of Rational Conformal Field Theories with respect to theA (1) N level one algebra.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Belavin, A. A., Polyakov, A. B., Zamolodchikov, A. B.: Infinite conformal symmetry in 2D field theory. Nucl. Phys. B241, 333–380 (1984)

    Google Scholar 

  2. Vafa, C.: Towards classification of conformal field theories. Phys. Lett. B.206, 421–426 (1988)

    Google Scholar 

  3. Moore, G., Seiberg, N.: Polynomial equations for rational conformal field theories. Phys. Lett.212, 451–460 (1988)

    Google Scholar 

  4. Moore, G., Seiberg, N.: Naturality in conformal field theory. Preprint IASSNS-HEP 88/31

  5. Moore, G., Seiberg, N.: Classical and quantum conformal field theory. Preprint IASSNS-HEP 88/35

  6. Verlinde, E.: Fusion rules and modular transformations in 2D CFT's. Nucl. Phys. B (FS 22)300, 360–376 (1988)

    Google Scholar 

  7. Itzykson, C.: Level one Kac-Moody characters and modular invariance. Conformal Field Theories and related topics. Binetruy, P., Sorba, P., Stora, R., (eds), Nucl., Phys. B. (Proc. Suppl.)5, pp. 150–165. Amsterdam: North-Holland 1988

    Google Scholar 

  8. Cappelli, A., Itzykson, C., Zuber, J. B.: The ADE classification ofA (1)1 and minimal conformal field theories. Commun. Math. Phys.113, 1–26 (1987)

    Google Scholar 

  9. Tsuchiya, A., Kanie, Y.: Vertex operators in CFT onPC1 and monodromy representations of the braid group. Lett. Math. Phys.13, 303 (1987)

    Google Scholar 

  10. Frenkel, I., Lepowsky, J., Meurman, A.: Vertex operators and the Monster. New York: Academic Press (to appear)

  11. Serre, J. P.: Représentation linéaire des groupes finis. Paris: Hermann 1968

    Google Scholar 

  12. Serre, J. P.: Cours d'arithmétique. Paris: PUF 1970

    Google Scholar 

  13. Gepner, D., Qiu, Z.: Modular invariant partition functions for parafermionic theories. Nucl. Phys. B. (FS 19)285, 423–453 (1987)

    Google Scholar 

  14. Dijkgraaf, R., Verlinde, E.: Modular invariance and the fusion algebra. Conformal Field Theories and related topics. Binetruy, P., Sorba, P., Stora, R., (eds). Nucl. Phys. B. (Proc. Suppl.)5, pp. 87–97 Amsterdam: North-Holland 1988

    Google Scholar 

  15. Lang, S.: Algebraic number theory. Reading, MA: Addison-Wesley 1970

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LPTENS, 24 rue Lhomond, F-75005, Paris, France

    P. Degiovanni

Authors
  1. P. Degiovanni
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by K. Gawedzki

Unité propre de Recherche du Centre National de la Recherche Scientifique, associée à l'Ècole Normale Supérieure et à l'Université de Paris-Sud

Rights and permissions

Reprints and permissions

About this article

Cite this article

Degiovanni, P. Z/NZ Conformal Field Theories. Commun.Math. Phys. 127, 71–99 (1990). https://doi.org/10.1007/BF02096494

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02096494

Keywords

Search

Navigation