Skip to main content
Log in

Modular covariance of minimal model correlation functions

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

Abstract

We prove that one-point functions of all scaling fields in minimal left-right diagonal models of conformal field theory are modular covariant. This consistency condition should allow one to extend these minimal models to Riemann surfaces of arbitrary genus.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Belavin, A.A., Polyakov, A.M., Zamolodchikov, A.B.: Infinite conformal symmetry in two-dimensional quantum field theory. Nucl. Phys.B241, 333–380 (1984)

    Google Scholar 

  2. Friedan, D., Shenker, S.: The analytic geometry of two-dimensional conformal field theory. Nucl. Phys.B281, 509–545 (1987); The integrable analytic geometry of quantum strings. Phys. Lett.175B, 287–296 (1986)

    Google Scholar 

  3. Eguchi, T., Ooguri, H.: Conformal and current algebra on a general Riemann surface. Nucl. Phys.B282, 308–328 (1987)

    Google Scholar 

  4. Cardy, J.: Operator content of two-dimensional conformal invariant theories. Nucl. Phys.B270, 186–204 (1986)

    Google Scholar 

  5. Cappelli, A., Itzykson, C., Zuber, J.-B.: The A-D-E classification of two-dimensional conformal invariant theories. Commun. Math. Phys.113, 1–26 (1987)

    Google Scholar 

  6. Dotsenko, Vl.S., Fateev, V.A.: Conformal algebra and multipoint correlation functions in 2d statistical models. Nucl. Phys.B240 [FS12], 312–348 (1984); Four-point correlation functions and operator algebra in 2d conformal invariant theories with central charge ≦1, Nucl. Phys.B251 [FS13], 691–734 (1985); Operator algebra of two-dimensional conformal theories with central chargeC≦1. Phys. Lett.154B, 291–295 (1985)

    Google Scholar 

  7. Zamolodchikov, A.B., Fateev, V.A.: Operator algebra and correlation functions in the two-dimensional SU(2)×SU(2) chiral Wess-Zumino model. Sov. J. Nucl. Phys.43, 657–664 (1986)

    Google Scholar 

  8. Sonoda, H.: Sewing conformal field theories I. Nucl. Phys.B311, 401–416 (1988/89); Sewing conformal field theories II. Nucl. Phys.B311, 417–432 (1988/89)

    Google Scholar 

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

    Google Scholar 

  10. Felder, G.: BRST approach to minimal models, ETH preprint (1988); Nucl. Phys. B (to appear)

  11. Bagger, J., Nemeschansky, D., Zuber, J.-B.: Minimal model correlation functions on the torus. USC-88/009 (1988)

  12. Jayaraman, T., Narain, K.S.: Correlation functions for minimal models on the torus. IC/88/306 (1988)

  13. Crnković, Č., Sotkov, G.M., Stanishkov, M.: Minimal models on hyperelliptic surfaces. ISAS-117/EP/88 (1988)

  14. Foda, O., Nieunhuis, B.: The Coulomb gas representation of critical RSOS models on the sphere and on the torus. THU-88-34 (1988)

  15. Di Francesco, P.: Structure constants for rational conformal field theories. Phys. Lett.215B, 124–128 (1988)

    Google Scholar 

  16. Felder, G., Fröhlich, J., Keller, G.: Braid matrices and structure constants for minimal conformal models, IAS/ETH preprint (1989)

  17. Andrews, G.E.: The theory of partitions. Encyclopedia of Mathematics and its Applications. London, Amsterdam, Don Mills (Ontario), Sidney, Toykyo: Addison-Wesley (1976)

    Google Scholar 

  18. Bernard, D.: On the Wess-Zumino-Witten model on the torus. Nucl. Phys.B303, 77–93 (1988)

    Google Scholar 

  19. Hurwitz, A., Courant, R.: Allgemeine Funktionentheorie und elliptische Funktionen. Berlin: Springer 1929

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by K. Gawedzki

Supported in part by NSF grant DMS 8610730

Rights and permissions

Reprints and permissions

About this article

Cite this article

Felder, G., Silvotti, R. Modular covariance of minimal model correlation functions. Commun.Math. Phys. 123, 1–15 (1989). https://doi.org/10.1007/BF01244015

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01244015

Keywords

Navigation