On the W-Gravity Spectrum and Its G-Structure

  • Peter Bouwknegt
  • Jim McCarthy
  • Krzysztof Pilch
Part of the NATO ASI Series book series (NSSB, volume 328)


We present results for the BRST cohomology of W[g] minimal models coupled to W[g] gravity, as well as scalar fields coupled to W[g] gravity. In the latter case we explore an intricate relation to the (twisted) g cohomology of a product of two twisted Fock modules.


Minimal Model Weyl Group Verma Module Ghost Number Weyl Chamber 
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  1. [1]
    P. Bouwknegt, J. McCarthy and K. Pilch, USC-93/11, hep-th/9302086, Lett. Math. Phys. 29 (1993), to be published.Google Scholar
  2. [2]
    P. Bouwknegt, J. McCarthy and K. Pilch, On the BRST structure of W 3 gravity coupled to c = 2 matter, USC-93/14, hep-th/9303164.Google Scholar
  3. [3]
    J. Thierry-Mieg, Phys. Lett. B197 (1987) 368.MathSciNetADSGoogle Scholar
  4. [4]
    M. Bershadsky, W. Lerche, D. Nemeschansky and N.P. Warner, Phys. Lett. B292 (1992) 35. WB.MathSciNetADSGoogle Scholar
  5. [5]
    V. Sadov, On the spectra of sl(N)k/sl(N)k -cosets and W N gravities, HUTP-92/A055, hep-th/9302060; The hamiltonian reduction of the BRST complex and N = 2 SUSY, HUTP-93/A006, hep-th/9304049.Google Scholar
  6. [6]
    O. Aharony, O. Ganor, J. Sonnenschein and S. Yankielowicz, Phys. Lett. B305 (1993) 35; and references therein.MathSciNetADSGoogle Scholar
  7. [7]
    M. Bershadsky, W. Lerche, D. Nemeschansky and N.P. Warner, Nucl. Phys. B401 (1993) 304.MathSciNetADSCrossRefGoogle Scholar
  8. [8]
    H. Lu, C.N. Pope, X.J. Wang and K.W. Wu, The complete spectrum of the W 3 string, CTP TAMU 50/93, hep-th/9309041, and references therein.Google Scholar
  9. [9]
    I.N. Berstein, I.M. Gel’fand and S.I. Gel’fand, in: Proc. Summer School of the Bolyai János Math. Soc., ed. I.M. Gel’fand (New York, 1975).Google Scholar
  10. [10]
    B.L. Feigin, Usp. Mat. Nauk 39 (1984) 195.MathSciNetzbMATHGoogle Scholar
  11. [11]
    B.L. Feigin and E.V. Frenkel, Comm. Math. Phys. 128 (1990) 161.MathSciNetADSzbMATHCrossRefGoogle Scholar
  12. [12]
    P. Bouwknegt, J. McCarthy and K. Pilch, J. Geom. Phys. 11 (1993) 225.MathSciNetADSzbMATHCrossRefGoogle Scholar
  13. [13]
    R. Bott, Ann. Math. 66 (1957) 203; B. Kostant, Ann. Math. 74 (1961) 329.MathSciNetzbMATHCrossRefGoogle Scholar
  14. [14]
    M. Wakimoto, Comm. Math. Phys. 104 (1986) 605.MathSciNetADSzbMATHCrossRefGoogle Scholar
  15. [15]
    P. Bouwknegt, J. McCarthy and K. Pilch, Prog. Theor. Phys. Suppl. 102 (1990) 67.MathSciNetADSCrossRefGoogle Scholar
  16. [16]
    J.E. Humphreys, Reflection groups and Coxeter groups, Cambridge University Press (1990).Google Scholar
  17. [17]
    O. Gabber and A. Joseph, Ann. Sci. Ec. Norm. Sup. 14 (1981) 261; B.D. Boa, Contemp. Math. 139 (1991) 1; K.J. Karlin, Trans. Amer. Math. Soc. 249 (1986) 29.MathSciNetzbMATHGoogle Scholar
  18. [18]
    D. Kazhdan and G. Lustig, Inv. Math. 53 (1979) 165.ADSzbMATHCrossRefGoogle Scholar
  19. [19]
    P. Bouwknegt and K. Schoutens, Phys. Rep. 223 (1993) 183.MathSciNetADSCrossRefGoogle Scholar
  20. [20]
    H. Lu, C.N. Pope and X.J. Wang, On higher-spin generalizations of string theory, CTP TAMU-22/93, hep-th/9304115; K. Hornfeck, Explicit construction of the BRST charge for W 4, DFTT-25/93, hep-th/9306019; C.-J. Zhu, The BRST quantization of the nonlinear 2 and W 4 algebras, SISSA/77/93/EP, hep-th/9306026.Google Scholar
  21. [21]
    B.H. Lian and G.J. Zuckerman, Phys. Lett. B254 (1991) 417; Phys. Lett. B266 (1991) 21; Comm. Math. Phys. 145 (1992) 561.MathSciNetADSGoogle Scholar
  22. [22]
    E. Frenkel, W-algebras and Langlands-Drinfel’d correspondence, in Proc. of the 1991 Cargèse workshop on “New Symmetry Principles in Quantum Field Theory,” eds. J. Fröhlich et. al., Plenum Press (1992).Google Scholar
  23. [23]
    M. Niedermaier, Comm. Math. Phys. 148 (1992) 249.MathSciNetADSzbMATHCrossRefGoogle Scholar
  24. [24]
    P. Bouwknegt, J. McCarthy and K. Pilch, Comm. Math. Phys. 145 (1992) 541.MathSciNetADSzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Peter Bouwknegt
    • 1
  • Jim McCarthy
    • 2
  • Krzysztof Pilch
    • 1
  1. 1.Department of Physics and AstronomyUniversity of Southern CaliforniaLos AngelesUSA
  2. 2.Department of Physics and Mathematical PhysicsUniversity of AdelaideAdelaideAustralia

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