Skip to main content
SpringerLink
Log in

Topological orbifold models and quantum cohomology rings

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

Abstract

We discuss the topological sigma model on an orbifold target space. We describe the moduli space of classical minima for computing correlation functions involving twisted operators, and show, through a detailed computation of an orbifold ofCP 1 by the dihedral groupD 4, how to compute the complete ring of observables. Through this procedure, we compute all the rings of dihedralCP 1 orbifolds. We then considerCP 2/D 4, and show how the techniques of topologicalanti-topological fusion might be used to compute twist field correlation functions for nonabelian orbifolds.

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. Atiyah, M.F., Bott, R.: Ann. Math.88, 451–491 (1968)

    Google Scholar 

  2. Berglund, P., Greene, B. Hübsch, T.: Classicalvs. Landau-Ginzburg Geometry of Compacification. CERN, U.T., and Harvard preprint CERN-TH-6381/92, UTTG-21-91, HUTMP-91/B315

  3. Candelas, P.: Lectures on Complex Manifolds. In: Proceedings of the Winter School on High Energy Physics, Puri, India

  4. Candelas, P., De La Ossa, X.C., Green P., Parkes, L.: Nucl. Phys.B359, 21–74 (1991)

    Google Scholar 

  5. Candelas, P., Horowitz, G., Strominger, A., Witten, E.: Nucl. Phys.B258, 46–74 (1985)

    Google Scholar 

  6. Cecotti, S., Vafa, C.: Nucl. Phys.B367, 359–461 (1991)

    Google Scholar 

  7. Cecotti, S., Vafa, C.: Phys. Rev. Lett68, 903–906 (1992)

    Google Scholar 

  8. Cecotti, S., Vafa, C.: Massive Orbifolds. SISSA and Harvard preprint SISSA 44/92/EP, HUTP-92/A013

  9. Cecotti, S., Vafa, C.: On Classification ofN=2 Supersymmetric Theories. Harvard and SISSA preprints HUTP-92/A064 and SISSA-203/92/EP

  10. Dijkgraaf, R., Verlinde, H., Verlinde, E.: Nucl. Phys.B352, 59–86 (1991)

    Google Scholar 

  11. Dixon, L., Harvey, J., Vafa, C., Witten, E.: Nucl. Phys.B261, 678–686 (1985), and Nucl. Phys.B274, 285–314 (1986); Dixon, L., Friedan, D., Martinec, E., Shenker, S.: Nucl Phys.B282, 13–73 (1987); Freed, D., Vafa, C.: Commun. Math. Phys.110, 349–389 (1987)

    Google Scholar 

  12. Fendley, P., Intrilligator, K.: Nucl. Phys.B372 533–558 (1992); Nucl. Phys.B380, 265–290 (1992)

    Google Scholar 

  13. Frakas, H.M., Kra, I.: Riemann Surfaces. Berlin, Heidelberg, New York: Springer 1980

    Google Scholar 

  14. Gato, B.: Nucl. Phys.B334, 414–430 (1990)

    Google Scholar 

  15. Greene, B.R., Plesser, M.R.: Nucl. Phys.B338, 15–37 (1990)

    Google Scholar 

  16. Greene, B.R., Vafa, C., Warner, N.: Nucl. Phys.B234, 271–390 (1989)

    Google Scholar 

  17. Hamidi, S., Vafa, C.: Nucl. Phys.B279, 465–513 (1989)

    Google Scholar 

  18. Intriligator, K., Vafa, C.: Nucl. Phys.B339, 95–120 (1990)

    Google Scholar 

  19. Its, A.R., Novokshenov, V.Yu.: The Isomonodromic Deformation Method in the Theory of Painlevé Equations. Lecture Notes in Mathematics1191, Berlin, Heidelberg, New York: Springer 1986; McCoy, B.M., Tracy, C.A. Wu, G.G.: Math Phys.18, 1058–1104 (1977)

    Google Scholar 

  20. Jackiw, R., Rebbi, C.: Phys. Rev.D13, 3398–3409 (1976); Goldstone, J., Wilczek, F.: Phys. Rev. Lett.47, 986–989 (1981)

    Google Scholar 

  21. Kitaev, A.V.: The Method of Isomonodromy Deformations for Degenerate Third Painlevé Equation. In: Questions of Quantum Field theory and Statistical Physics 8, (Zap. Nauch. Semin. LOMI v. 161), Popov, V.N., Kulish P.P. (eds.) Leningrad: Nauka

  22. Leaf-Herrmann, W.A.: Harvard preprint HUTP-91/AO61

  23. Lerche, W., Vafa, C., Warner, N.: Nucl. Phys.B324, 427–474 (1989)

    Google Scholar 

  24. Mackey, G.: Acta Math.99, 265–311 (1958)

    Google Scholar 

  25. Narain, K.S.: Nucl. Phys.B243, 131–156 (1984)

    Google Scholar 

  26. Roan, S.-S.: Intl. J. Math. (2)1, 211–232 (1990)

    Google Scholar 

  27. Roan, S.-S.: Intl. J. Math. (4)2, 439–455 (1991)

    Google Scholar 

  28. Slodowy, P.: Simple Singularities and Simple Algebraic Groups. Lecture Notes in Mathematics815, Berlin, Heidelberg, New York: Springer 1980; McKay, J.: Cartan Matrices, Finite Groups of Quaternions, and Kleinian Singularities. Proc. Am. Math. Soc.153 (1981)

    Google Scholar 

  29. Vafa, C.: Mod. Phys. Lett.A4, 1169–1185 (1989)

    Google Scholar 

  30. Wen, X.-G., Witten, E.: Nucl. Phys.B261, 651–677 (1985)

    Google Scholar 

  31. Witten, E.: Mirror Manifolds and Topological Field Theory. Institute for Advanced Studies preprint IASSNS-HEP 91/83

  32. Witten, E.: Nucl. Phys.B202, 253–316 (1982)

    Google Scholar 

  33. Witten, E.: Nucl. Phys.B258, 75–100 (1985)

    Google Scholar 

  34. Zamolodchikov, A.B.: JETP Lett.43, 730–732 (1986)

    Google Scholar 

  35. Zaslow, E.: Harvard preprint HUTP-93/A010

Download references

Author information

Authors and Affiliations

  1. Lyman Laboratory of Physics, Harvard University, 02138, Cambridge, MA, USA

    Eric Zaslow

Authors
  1. Eric Zaslow
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by N.Yu. Reshetikin

Supported in part by Fannie and John Hertz Foundation

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zaslow, E. Topological orbifold models and quantum cohomology rings. Commun.Math. Phys. 156, 301–331 (1993). https://doi.org/10.1007/BF02098485

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02098485

Keywords

Search

Navigation