q-Deformation of SU(1,1) Conformal Ward Identities and q-Strings

  • André LeClair
Part of the NATO ASI Series book series (NSSB, volume 245)


We define a q-deformation of the SU(1, 1) Ward identities of 2d conformally invariant field theory based on the quantum SU(1,1) algebra. The deformation preserves the main properties of the conformai Ward identities, namely that the two and three point functions are completely determined. A connection with a q-deformation of the Veneziano amplitude is revealed.


Hopf Algebra Quantum Group Vertex Operator Ward Identity Conformal Symmetry 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    D. Bernard and A. LeClair, Princeton University preprint PUPT-1123, to appear in Physics Letters B.Google Scholar
  2. [2]
    L. J. Romans, A New Family of Dual Models (‘q-strings’), Univ. Southern Cal. Preprint USC-88/HEP014.Google Scholar
  3. [3]
    D. D. Coon and Simon Yu, Phys. Rev. D 10 (1974) 3780, and references therein.ADSCrossRefGoogle Scholar
  4. [4]
    A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, Nucl. Phys. B241 (1984) 333.MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    P. P. Kulish and N. Yu. Reshetikhin, J. Soviet Math. 23 (1983) 2435.CrossRefGoogle Scholar
  6. [6]
    M. Jimbo, Lett. Math. Phys. 10 (1985) 63.MathSciNetADSMATHCrossRefGoogle Scholar
  7. [7]
    V. G. Drinfel’d, Doklady Akad. Nauk. SSSR 283 (1985) 1060.MathSciNetGoogle Scholar
  8. [8]
    E. K. Sklyanin, Funct. Anal. Appl. 17 (1983) 34.MathSciNetGoogle Scholar
  9. [9]
    G. E. Andrews, q-stries: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics, and Computer Algebra, AMS Regional Conference Series 66 (1986).Google Scholar
  10. [10]
    V. G. Drinfel’d, Sov. Math. Dokl. 36 (1988) 212.MathSciNetMATHGoogle Scholar
  11. [11]
    I. B. Frenkel and N. Jing, Vertex Representations of Quantum Affine Algebras, Yale Math. Preprint, (1988)Google Scholar
  12. [12]
    D. Bernard, Lett. Math. Phys. 17 (1989)Google Scholar
  13. [13]
    M. B. Green, J. H. Schwarz, and E. Witten, Superstring Theory I, Cambridge University Press (1987).Google Scholar
  14. [14]
    Talk delivered at this conference, and references therein.Google Scholar
  15. [15]
    S. L. Woronowicz, Comm. Math. Phys. 111 (1987) 613.MathSciNetADSMATHCrossRefGoogle Scholar
  16. [16]
    Yu. Manin, Quantum Groups and Non-Commutative Geometry, in Publication du Centre de Recherches Mathématiques, (1988).Google Scholar
  17. [17]
    T. Masuda et al., C. R. Acad. Sci. Paris, t.307, Série I, p559, 1988.MathSciNetMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • André LeClair
    • 1
  1. 1.Newman LaboratoryCornell UniversityIthacaUSA

Personalised recommendations