Superstrings pp 169-186 | Cite as

Liouville Strings

  • Jean-Loup Gervais
Part of the NATO ASI Series book series (NSSB, volume 175)


In 1981 Polyakov [1,2] showed that the integration measure over surfaces embedded into flat space-times of dimension D not equal to 26 ( or 10), involves an additional scalar field with an exponential potential. With this motivation I, together with A. Neveu [3–8] and A. Bilal [9–12], extensively studied this so-called Liouville dynamics and developed the associated string theories, which are of a novel type. As we shall see, two new critical values of the space-time dimension D appea, r both for the purely bosonic and for the Neveu-Schwarz-Ramond (NSR) case. They are equal to 7 and 13, and to 3 and 5 respectively. Our results possess an interesting structure which I intend to summarize, as much as posssible, in the present lecture notes.




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  1. [1]
    A.M. Polyakov, Phys.Lett. 103B(1981)207.MathSciNetADSGoogle Scholar
  2. [2]
    A.M. Pokyakov, Phys.Lett. 103B(1981)211.ADSGoogle Scholar
  3. [3]
    J.-L. Gervais, A. Neveu, Nucl.Phys. B199(1982)59; B209 (1982) 125.MathSciNetADSCrossRefGoogle Scholar
  4. [4]
    J.-L. Gervais, A. Neveu, Nucl.Phys. B209(1982)125.MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    J.-L. Gervais, A. Neveu, Nucl.Phys. B238(1984)125; 396MathSciNetADSCrossRefGoogle Scholar
  6. [6]
    J.-L. Gervais, A. Neveu, Nucl.Phys. B257[FS14](1985)59.MathSciNetADSCrossRefGoogle Scholar
  7. [7]
    J.-L. Gervais, A. Neveu, Phys.Lett. 151B(1985)271.MathSciNetADSGoogle Scholar
  8. [8]
    J.-L. Gervais, A. Neveu, Com.Math.Phys. 100 (1985) 15; Nucl. Phys. B264 (1986) 557Google Scholar
  9. [9]
    A. Bilal, J.-L. Gervais, Nucl.Phys. B284(1987)397.MathSciNetADSCrossRefGoogle Scholar
  10. [10]
    A. Bilal, J.-L. Gervais, Phys.Lett. 187B(1987)39.MathSciNetADSGoogle Scholar
  11. [11]
    A. Bilal, J.-L. Gervais, Nucl.Phys. B293(1987)1.MathSciNetADSCrossRefGoogle Scholar
  12. [12]
    A. Bilal, J.-L. Gervais, Liouville superstring and Ising model in three dimensions; preprint LPTENS 87/26.Google Scholar
  13. [13]
    L. Brink, P. di Vecchia, P. Howe, Phys.Lett. 65B(1976)471ADSGoogle Scholar
  14. [14]
    see, e.g., A.S. Schwartz Com.Math.Phys. 64(1979)233.Google Scholar
  15. [15]
    J.-L. Gervais, B. Sakita, Nucl.Phys. B34(1971)477.MathSciNetADSCrossRefGoogle Scholar
  16. [16]
    A. Belavin, A. Polyakov, A. Zamolodchikov, Nucl.Phy.B241 (1980)333.MathSciNetADSGoogle Scholar
  17. [17]
    V.G. Kac, Proc. Int. Congress of Mathematicians, 1978 Helsinki; Lecture Notes in Physics, vol. 94 (Springer, New York, 1979) p. 441.Google Scholar
  18. [18]
    Higher Transcendental Functions, Erdélyi, Magnus, Oberhetinger, Tricomi, Bateman Project, Vol.2, McGraw—Hill 955.Google Scholar
  19. [19]
    F. Gliozzi, D. Olive, J. Scherk, Nucl.Phys.B122(1977) 253ADSCrossRefGoogle Scholar
  20. [20]
    J.F. Arvis, Nucl.Phys.B212(1983)151; B218(1983)309.MathSciNetADSCrossRefGoogle Scholar
  21. [21]
    O. Babelon, Phys.Lett.141B(1984)353; Nucl.Phys. B258 (1985) 680.MathSciNetADSGoogle Scholar
  22. [22]
    For a pedagogical review, see P. Goddard, D. Olive, Int. J. Mod. Phys.A1 (1986) 303.MathSciNetADSGoogle Scholar
  23. [23]
    P. Goddard, W. Nahm, D. Olive, A. Schwimmer, Comm.Math. Phys.107(1986)179; A. Schwimmer in sProceedings of the 1985 Bonn Firenze Johns Hopkins meeting, World Scientific; P. Goddard, D. Olive, A. Schwimmer, Phys. Lett. 157B(1985)393MathSciNetADSMATHCrossRefGoogle Scholar
  24. [24]
    M. Ademollo, L. Brink, A. D’Adda, R. D’Auria, E. Napolitano, S. Sciuto, E. Del Giudice, P. Di Vecchia, S. Ferrara, F. Gliozzi, R. Musto, R. Pettorino, Nucl.Phys. B114 (1976) 297.ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1988

Authors and Affiliations

  • Jean-Loup Gervais
    • 1
  1. 1.Physique Théorique Ecole Normale SupérieureParisFrance

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