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Quantum Groups pp 259-276 | Cite as

Quantum group symmetry of 2D gravity

  • Jean-Loup Gervais
II. Quantum Groups, Symmetries Of Dynamical Systems And Conformal Field Theory
Part of the Lecture Notes in Mathematics book series (LNM, volume 1510)

Abstract

Current progresses in understanding quantum gravity from the operator viewpoint are reviewed. They are based on the U q (sl(2))-quantum-group structure recently put forward[1,2] for the chiral components of the metric in the conformal gauge.

Keywords

Quantum Group Poisson Bracket Conformal Weight Primary Field Liouville Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    O. Babelon, Phys. Lett. B215 (1988), 523.MathSciNetCrossRefGoogle Scholar
  2. [2]
    J.-L. Gervais, Commun. Math. Phys. 130 (1990), 257.MathSciNetCrossRefGoogle Scholar
  3. [3]
    J.-L. Gervais and B. Rostand, Nucl. Phys. B346 (1990), 473.MathSciNetCrossRefGoogle Scholar
  4. [4]
    J.-L. Gervais, Phys. Lett. B243 (1990), 85.MathSciNetCrossRefGoogle Scholar
  5. [5]
    J.-L. Gervais, Solving the strongly coupled 2D gravity: unitary truncation and quantum group structure, LPTENS preprint 90/13; Commun. Math. Phys. (to appear).Google Scholar
  6. [6]
    E. Cremmer, J.-L. Gervais, The quantum strip: Liouville theory for open strings, LPTENS preprint 90/32; Commun. Math. Phys. (to appear).Google Scholar
  7. [7]
    see A. Alekseev, L. Faddeev, M. Semenov-Tian-Shansky and A. Volkov, The unravelling of the quantum group structure in the WZNW theory, CERN preprint TH-5981/91 and refs therein.Google Scholar
  8. [8]
    J.-L. Gervais and A. Neveu, Nucl. Phys. B257[FS14] (1985), 59.MathSciNetCrossRefGoogle Scholar
  9. [9]
    J.-L. Gervais and A. Neveu, Phys. Lett. 151B (1985), 271.MathSciNetCrossRefGoogle Scholar
  10. [10]
    J.-L. Gervais and A. Neveu, Nucl. Phys. B199 (1982), 59.MathSciNetCrossRefGoogle Scholar
  11. [11]
    J.-L. Gervais and A. Neveu, Nucl. Phys. B202 (1982), 125.MathSciNetCrossRefGoogle Scholar
  12. [12]
    J.-L. Gervais and A. Neveu, Nucl. Phys. B224 (1983), 329.MathSciNetCrossRefGoogle Scholar
  13. [13]
    J.-L. Gervais and A. Neveu, Nucl. Phys. B238 (1984), 125; Nucl. Phys. B238 (1984), 396.MathSciNetCrossRefGoogle Scholar
  14. [14]
    J.-L. Gervais and A. Neveu, Nucl. Phys. B264 (1986), 557.MathSciNetCrossRefGoogle Scholar
  15. [15]
    J.-L. Gervais, Liouville Superstrings, Perspectives in string the proceedings of the Niels Bohr, World Scientific, Nordita Meeting, 1987; DST workshop on particle physics-Superstring theory, proceedings of the I.I.T. Kanpur meeting, World Scientific, 1987. J.-L. Gervais, Systematic approach to conformal theories, Nucl. Phys. B (Proc. Supp.) 5B (1988), 119–136. A. Bilal and J.-L. Gervais, Conformal theories with non-linearly-extended Virasoro symmetries and Lie-algebra classification, Conference Proceedings: “Infinite dimensional Lie algebras and Lie groups” (V. Kac, Marseille, eds.), World-Scientific, 1988.Google Scholar
  16. [16]
    E. Cremmer, J.-L. Gervais, Commun. Math. Phys. 134 (1990), 619.MathSciNetCrossRefGoogle Scholar
  17. [17]
    see, e.g. B. Feigin and E. Frenkel, Quantization of the Drinfeld-Sokolov reduction, Harvard preprint (to appear) Phys. Lett. B.Google Scholar
  18. [18]
    E. Sklyanin, J.Phys. A 21 (1988), 2375.MathSciNetGoogle Scholar
  19. [19]
    I. Cherednik, Theor.Math.Phys. 61 (1984), 977.MathSciNetCrossRefGoogle Scholar
  20. [20]
    G. Andrews, Conference board of the math. sciences, Regional conference series in math., vol. 66, A.M.S..Google Scholar
  21. [21]
    A. Bilal and J.-L. Gervais, Nucl. Phys. B284 (1987), 397; Phys. Lett. B187 (1987), 39; for reviews see [15], Nucl. Phys. B293 (1987), 1.MathSciNetCrossRefGoogle Scholar
  22. [22]
    A. Bilal and J.-L. Gervais, Nucl. Phys. B295[FS21] (1988), 277.MathSciNetCrossRefGoogle Scholar
  23. [23]
    J.-L. Gervais and B. Rostand, On two-dimensional supergravity and the super Möbius group, preprint LPTENS 91/3,; Commun. Math. Phys. (to appear).Google Scholar
  24. [24]
    J.-L. Gervais, Gravity matter couplings from Liouville theory, LPTENS preprint (to appear).Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Jean-Loup Gervais
    • 1
  1. 1.Laboratoire de Physique Théorique de l'École Normale SupérieureParis, Cedex 05France

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