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The Conformal Block Structure of Perturbation Theory in Two Dimensions

  • Rainald Flume
Chapter
  • 173 Downloads
Part of the Mathematical Physics Studies book series (MPST, volume 13)

Abstract

We describe some field theoretical aspects of marginal and relevant interactions perturbing two-dimensional conformally invariant field theories. Repercussions of the critical (non-Gaussian) fixed point theory for the structure of the perturbation series and in particular deformations of braid group representations in the perturbed theory are investigated. Some speculations about the importance of those deformations for an adequate understanding of renormalisation group flows in various models are added.

Keywords

Vertex Operator Conformal Block Braid Group Tensor Factor Order Perturbation Theory 
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References

  1. [1]
    A. A. Belavin, A. M. Polyakov and A. B. Zamolodchikov, Nucl. Phys. B241 (1984),333.MathSciNetADSCrossRefGoogle Scholar
  2. [2]
    A. B. Zamolodchikov, JETP Lett. 43 (1988) 730.MathSciNetADSGoogle Scholar
  3. [3]
    J. L. Cardy, Nucl. Phys. B270 (1986) 186.MathSciNetADSCrossRefGoogle Scholar
  4. [4]
    A. Ludwig, Nucl. Phys. B285 (1987) 97.MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    A. Ludwig and J. L. Cardy, Nucl. Phys. B285 (1987) 687.MathSciNetADSCrossRefGoogle Scholar
  6. [6]
    L. P. Kadanoff, J. Phys. A11 (1978) 1399.MathSciNetADSGoogle Scholar
  7. [7]
    L. P. Kadanoff and A. C. Brown, Ann. Phys. 121 (1979) 318.ADSCrossRefGoogle Scholar
  8. [8]
    A. B. Zamolodchikov, Int. J. Mod. Phys. A4 (1989) 4235.MathSciNetADSGoogle Scholar
  9. [9]
    P. Christe and G. Mussardo, Int. J. Mod. Phys. A5 (1990) 4581 and references therein.MathSciNetADSGoogle Scholar
  10. [10]
    F. Constantinescu and R. Flume, J. Phys. A23 (1990) 2971.MathSciNetADSGoogle Scholar
  11. [11]
    P. Chaselon, F. Constantinescu and R. Flume, Phys. Lett. B257 (1991) 63.MathSciNetADSGoogle Scholar
  12. [12]
    G. Moore and N. Seiberg, Phys. Lett. 122B (1988) 451.MathSciNetADSGoogle Scholar
  13. [13]
    K. H. Rehren and B. Schroer, Nuc. Phys. B295 (1988) 229; Commun. Math. Phys. 116 (1988) 675.MathSciNetADSCrossRefGoogle Scholar
  14. [14]
    G. Felder, J. Frohlich and G. Keller, Commun. Math. Phys. 124 (1989) 417; Commun. Math. Phys. 130 (1990) 1.MathSciNetADSzbMATHCrossRefGoogle Scholar
  15. [15]
    E. Speer,Generalized Feynman Amplitudes, Annals of Mathematical Studies Vol. 62(1969).Google Scholar
  16. [16]
    G. Felder, Nucl. Phys. B317 (1989) 215.MathSciNetADSCrossRefGoogle Scholar
  17. [17]
    S. D. Mathur, preprint HUTMP-90-B-299 (1990).Google Scholar
  18. [18]
    F. Constantinescu and M. Lüdde, Braid Modules, preprint Bonn HE–91–15.Google Scholar
  19. [19]
    J. Birman, “Braids, Links and mapping class groups”, Princeton UP (1974).Google Scholar
  20. [20]
    D. A. Kastor, E. J. Martinec and S. H. Shenker, Nuclear Phys. 316 (1989) 590.MathSciNetADSCrossRefGoogle Scholar
  21. [21]
    R. G. Pogossyan, Study of the vicinities of super conformal fixed points in two-dimensional field theory, Yerevan preprint ePhN–1003 53-87 (1987).Google Scholar
  22. [22]
    A. Cappelli, J. I. Latorre Nucl. Physics B340 (1990) 659.MathSciNetADSGoogle Scholar
  23. [23]
    V. P. Yurov and Al. B. Zamolodchikov, Int. J. Mod. Phys. A5 (1990) 3221.ADSGoogle Scholar
  24. [24]
    Al. B. Zamolodchikov, Nucl. Phys. B342 (1990) 695.MathSciNetADSCrossRefGoogle Scholar
  25. [25]
    M. Henkel and J-Saleur, J. Phys. A: Math. Gen. 22 (1989) L513.MathSciNetADSCrossRefGoogle Scholar
  26. [26]
    G. Von Gehlen, Nucl. Phys. B330 (1990) 741.ADSCrossRefGoogle Scholar
  27. [27]
    D. Bernard, Quantum symmetries in 2-D massive field theories, preprint Saclay SPh-T–91–124 (1991).Google Scholar
  28. [28]
    E. Witten, Commun. Math. Phys. 92 81994 455.Google Scholar
  29. [29]
    D. J. Gross and A. Neveu, Phys. Rev. D10 (1974) 3235.ADSGoogle Scholar
  30. [30]
    S. Chauduri and J. A. Schwarz, preprint CLNS 88/851 (1988).Google Scholar
  31. [31]
    M. Luscher and K. Pohlmeyer, Nucl. Phys. B137 (1978) 46.MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1992

Authors and Affiliations

  • Rainald Flume
    • 1
  1. 1.Physikalisches InstitutBonn 1Germany

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