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Semi-infinite cohomology ofW-algebras

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Abstract

We generalize some of the standard homological techniques toW-algebras, and compute the semi-infinite cohomology of theW 3 algebra on a variety of modules. These computations provide physical states inW 3 gravity coupled toW 3 minimal models and to two free scalar fields.

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References

  1. Thierry-Mieg, J.,Phys. Lett. 197B, 368 (1987).

    Google Scholar 

  2. Das, S. R., Dhar, A., and Rama, S. K.,Modern Phys. Lett. A6, 3055 (1991);Int. J. Mod. Phys. A7, 2295 (1992); Rama, S. K.,Modern Phys. Lett. A6, 3531 (1991).

    Google Scholar 

  3. Pope, C. N., Romans, L. J., and Stelle, K. S.,Phys. Lett. 268B, 167 (1991);Phys. Lett. 269B, 287 (1991); Pope, C. N., Romans, L. J., Sezgin, E., and Stelle, K. S.,Phys. Lett. 274B, 298 (1992); Lu, H., Pope, C. N., Schrans, S., and Xu, K. W.,Nuclear Phys. B385, 99 (1992); Lu, H., Pope, C. N., Schrans, S., and Wang, X. J.,Nuclear Phys. B379, 47 (1992).

    Google Scholar 

  4. Bershadsky, M., Lerche, W., Nemeschansky, D., and Warner, N. P.,Phys. Lett. 292B, 35 (1992).

    Google Scholar 

  5. Bergshoeff, E., Sevrin, A., and Shen, X.,Phys. Lett. 296B, 95 (1992); de Boer, J. and Goeree, J., KPZ analysis forW 3 gravity, preprint THU-92/34.

    Google Scholar 

  6. Pope, C. N., Sezgin, E., Stelle, K. S., and Wang, X. J.,Phys. Lett. 299B, 247 (1993); West, P., On the spectrum, no ghost theorem and modular invariance ofW 3 strings, KCL-TH-92-7; Lu, H., Nilsson, B. E. W., Pope, C. N., and West, P. C., The low-level spectrum of theW 3 string, CTP TAMU-70/92; Lu, H., Pope, C. N., Schrans, S., and Wang, X. J., On the spectrum and scattering ofW 3 strings, CTP TAMU-4/93; The interactingW 3 string, CTP TAMU-86/92.

    Google Scholar 

  7. Bershadsky, M., Lerche, W., Nemeschansky, D., and Warner, N. P., ExtendedN = 2 superconformal structure of gravity andW-gravity coupled to matter, CALT-68-1832.

  8. Witten, E., Nuclear Phys.B373, 187 (1992); Witten, E. and Zwiebach, B.,Nuclear Phys. B377, 55 (1992).

    Google Scholar 

  9. Bouwknegt, P., McCarthy, J., and Pilch, K., On BRST structure ofW 3 gravity coupled toc = 2 matter, VSC-93/14.

  10. Seiberg, N.,Prog. Theor. Phys. Suppl. 102, 319 (1990).

    Google Scholar 

  11. Bouwknegt, P. and Schoutens, K.,Phys. Rep. 223, 183 (1993).

    Google Scholar 

  12. Tsuchiya, A. and Kanie, Y.,Publ. RIMS, Kyoto Univ. 22, 259 (1986).

    Google Scholar 

  13. Frenkel, E.,Phys. Lett. 285B, 71 (1992).

    Google Scholar 

  14. Bouwknegt, P., McCarthy, J., and Pilch, K., Some aspects of free field resolutions in 2D CFT with application to the quantum Drinfeld-Sokolov reduction, in N. Berkovitzet al. (eds.),Proc. ‘Strings and Symmetries 1991’, World Scientific, Singapore, 1991.

    Google Scholar 

  15. Frenkel, E., Kac, V. G., and Wakimoto, M.,Comm. Math. Phys. 147, 295 (1992).

    Google Scholar 

  16. Watts, G. M. T.,Nuclear Phys. B326, 648 (1989); erratum,Nuclear Phys. B336, 720 (1990).

    Google Scholar 

  17. Bouwknegt, P., McCarthy, J., and Pilch, K.,J. Geom. Phys. 11, 225 (1993).

    Google Scholar 

  18. Knapp, A.,Lie Groups, Lie Algebras, and Cohomology, Princeton University Press, Princeton, 1988.

    Google Scholar 

  19. Humphreys, J. E.,Reflection Groups and Coxeter Groups, Cambridge University Press, Cambridge, 1990.

    Google Scholar 

  20. Bouwknegt, P., McCarthy, J., and Pilch, K.,Comm. Math. Phys. 145, 541 (1992).

    Google Scholar 

  21. Lian, B. H. and Zuckerman, G. J.,Phys. Lett. 254B, 417 (1991);Phys. Lett. 266B, 21 (1991);Comm. Math. Phys. 145, 561 (1992).

    Google Scholar 

  22. Marshakov, A., Mironov, A., Morozov, A., and Olshanetsky, M.,c =r G theories ofW G -gravity: the set of observables as a model of simply lacedG, FIAN/TD-02/92.

  23. Zhelobenko, D. B.,Compact Lie Groups and their Representations, American Mathematical Society, Providence, RI, 1973.

    Google Scholar 

  24. Itoh, K., SL(2, ℝ) current algebra and spectrum in two dimensional gravity, CTP-TAMU-42/91.

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Author information

Authors and Affiliations

  1. Department of Physics and Astronomy, University of Southern California, 90089-0484, Los Angeles, CA, USA

    Peter Bouwknegt & Krzysztof Pilch

  2. Department of Physics and Mathematical Physics, University of Adelaide, 5001, Adelaide, SA, Australia

    Jim McCarthy

Authors
  1. Peter Bouwknegt
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  2. Jim McCarthy
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  3. Krzysztof Pilch
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Additional information

Supported by the Packard Foundation.

Supported by the Australian Research Council.

Supported in part by the Department of Energy Contract # DE-FG03-84ER-40168.

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Bouwknegt, P., McCarthy, J. & Pilch, K. Semi-infinite cohomology ofW-algebras. Lett Math Phys 29, 91–102 (1993). https://doi.org/10.1007/BF00749725

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  • DOI: https://doi.org/10.1007/BF00749725

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