New Modular Representations and Fusion Algebras from Quantized SL(2,R) Chern-Simons Theories

  • Camillo Imbimbo
Part of the NATO ASI Series book series (NSSB, volume 310)


We consider the quantum-mechanical algebra of observables generated by canonical quantization of SL(2, R) Chern-Simons theory with rational charge on a space manifold with torus topology. We produce modular representations generalizing the representations associated to the SU(2) WZW models and we exhibit the explicit polynomial representations of the corresponding fusion algebras. The relation to Kac-Wakimoto characters of highest weight \( \widehat{sl}\left( 2 \right) \)(2) representations with rational level is illustrated.


Conformal Field Theory Fusion Rule Current Algebra Modular Representation Flat Connection 
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  1. [1]
    E. Witten, Comm. Math. Phys. 121 (1988) 351.Google Scholar
  2. [2]
    S. Elitzur, G. Moore, A. Schwimmer and N. Seiberg, Nucl. Phys. B326 (1989) 108.MathSciNetADSCrossRefGoogle Scholar
  3. [3]
    M. and V.P. Nair, Phys. Lett. B223 (1989) 61; Int. J. Mod. Phys. A5 (1990) 959.MathSciNetCrossRefGoogle Scholar
  4. [4]
    S. Axelrod, S. Della Pietra and E. Witten, J. Diff. Geom. 33 (1991) 787.MATHGoogle Scholar
  5. [5]
    H. Verlinde, Princeton preprint, PUTP-89/1140, unpublished.Google Scholar
  6. [6]
    E. Verlinde and H. Verlinde, Princeton preprint, PUTP-89/1149, unpublished.Google Scholar
  7. [7]
    C. Imbimbo, in: “String Theory and Quantum Gravity `91,” H. Verlinde, ed., World Scientific, Singapore (1992).Google Scholar
  8. [8]
    C. Imbimbo, Nucl. Phys. B384 (1992) 484.MathSciNetADSCrossRefGoogle Scholar
  9. [9]
    P. Furlan, R. Paunov, A.Ch. Ganchev and V.B. Petkova, Phys. Lett. 276 (1991) 63; A.Ch. Ganchev and V.B. Petkova, Trieste preprint, SISSA-111/92/EP.Google Scholar
  10. [10]
    C. Imbimbo, Phys. Lett. B258 (1991) 353.MathSciNetGoogle Scholar
  11. [11]
    E. Witten, Comm. Math. Phys. 137 (1991) 29.MATHGoogle Scholar
  12. [12]
    E. Witten, Nucl. Phys. B371 (1991) 191.MathSciNetADSCrossRefGoogle Scholar
  13. [13]
    G. ‘t Hooft, Nucl. Phys. B138 (1978) 1.ADSCrossRefGoogle Scholar
  14. [14]
    R. Jengo and K. Lechner, Phys. Rep. 213 (1992) 179.MathSciNetADSCrossRefGoogle Scholar
  15. [15]
    N. Woodhouse, “Geometric Quantization,” Oxford University Press, Oxford (1980).Google Scholar
  16. [16]
    V.G. Kac, “Infinite Dimensional Lie Algebras,” Cambridge University Press, Cambridge (1985).Google Scholar
  17. [17]
    V.G. Kac and M. Wakimoto, Proc. Nat. Acad. Sci. 85 (1988) 4956.MathSciNetADSMATHCrossRefGoogle Scholar
  18. [18]
    S. Mukhi and S. Panda, Nucl. Phys. B338 (1990) 263.MathSciNetADSCrossRefGoogle Scholar
  19. [19]
    E. Verlinde, Nucl. Phys. B300 (1988) 360.MathSciNetADSMATHCrossRefGoogle Scholar
  20. [20]
    B. Lian and G. Zuckerman, Phys. Lett. B254 (1991) 417.MathSciNetMATHGoogle Scholar
  21. [21]
    D. Gepner, Comm. Math. Phys. 141 (1991) 381.MATHGoogle Scholar
  22. [22]
    P. Di Francesco and J.-B. Zuber, Saclay preprint 92/138, hep-th/9211138.Google Scholar

Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Camillo Imbimbo
    • 1
  1. 1.Sezione di GenovaI.N.F.N.GenovaItaly

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