Skip to main content
SpringerLink
Log in

Relating Kac-Moody, Virasoro and Krichever-Novikov algebras

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

Abstract

We demonstrate that the Kac-Moody and Virasoro-like algebras on Riemann surfaces of arbitrary genus with two punctures introduced by Krichever and Novikov are in two ways linearly related to Kac-Moody and Virasoro algebras onS 1. The two relations differ by a Bogoliubov transformation, and we discuss the connection with the operator formalism.

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. M., Zamolodchikov, A. B.: Nucl. Phys.B241, 333 (1984)

    Google Scholar 

  2. Vafa, C.: Phys. Lett.190B, 47 (1987); Ishibashi, N., Matsuo, Y., Ooguri, H.: Mod. Phys. Lett.A2, 119 (1987); Segal, G.: Talk presented at the conference “Links between geometry and mathematical physics,” held at Schloss Rindberg and based on joint work with Quillen, D. (March 1987); Alvarez-Gaumé, L., Gomez, C., Moore, G., Vafa, C.: Nucl. Phys.B303, 455 (1988)

    Google Scholar 

  3. Dijkgraaf, R., Verlinde, E., Verlinde, H.: Commun. Math. Phys.115, 649 (1988)

    Google Scholar 

  4. West, P.: A review of duality, string vertices, overlap identities and the group theoretic approach to string theory. Cargese lectures 1987, CERN preprint TH 4819/87 (1987); Neveu, A., West, P.: Phys. Lett.179B, 235 (1986);180B, 34 (1986); Commun. Math. Phys.114, 613 (1988)

  5. Krichever, I. M., Novikov, S. P.: Funk. Anal. i. Pril.21, (2) 46 (1987); Krichever, I. M., Novikov, S. P.: Virasoro-type algebras, Riemann surfaces and strings in Minkowski space. Funk. Anal. i. Pril.21, (4) 47 (1987)

    Google Scholar 

  6. Fay, J. D.: Theta functions on Riemann surfaces. Springer Notes in Mathematics, vol.352. Berlin, Heidelberg, New York: Springer 1973; Mumford, D.: Tata lectures on Theta functions. Vol.1, 2 Boston: Birkhauser 1983

    Google Scholar 

  7. Witten, E.: Commun. Math. Phys.113, 529 (1988)

    Google Scholar 

  8. Segal, G.: Commun. Math. Phys.80, 301 (1981)

    Google Scholar 

  9. Verlinde, E., Verlinde, H.: private communication

Download references

Author information

Authors and Affiliations

  1. Theory Division CERN, CH-1211, Geneva 23, Switzerland

    José Alberty, Anne Taormina & Pierre van Baal

Authors
  1. José Alberty
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anne Taormina
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pierre van Baal
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by L. Alvarez-Gaumé

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alberty, J., Taormina, A. & van Baal, P. Relating Kac-Moody, Virasoro and Krichever-Novikov algebras. Commun.Math. Phys. 120, 249–260 (1988). https://doi.org/10.1007/BF01217964

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01217964

Keywords

Search

Navigation