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A BRST lagrangian quantization of reducible gauge theories: Non-abelianp-forms and string field theories

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Il Nuovo Cimento A (1965-1970)

Summary

By a suitable deformation of the reducible BRST algebra of the Abelianp-forms we obtain an explicit nilpotent BRST for the corresponding open reducible non-Abelianp-forms theory. We consider the Freedman-Townsend model and the corresponding (topological) massless limit. This allows us to perform a standard BRST quantization of the theory which avoids the Batalin-Vilkovisky formalism. This procedure leads to the introduction of auxiliary fields (related to BV antifields) which assume a universal form in terms of a single object belonging to the universal enveloping algebra. The auxiliary fields are interpreted as a sort of connection. A formal extension to the case of string field theory is presented.

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References

  1. C. Becchi, A. Rouet andR. Stora:Commun. Math. Phys.,42, 127 (1975);I. V. Tyutin: P. N. Lebedev Physical Institute preprint N. 39 (1975), unpublished.

    Article  MathSciNet  ADS  Google Scholar 

  2. R. Stora: inNew Developments in Quantum Field Theory and Statistical Mechanics, Cargèse 1976, edited byM. Lèvy andP. Mitter, NATO ASI Ser. B, Vol.26 (Plenum Press, New York, N.Y., 1976); inProgress in Gauge Field Theory, Cargèse 1983, edited byG. ’t Hooft et al., NATO ASI Ser. B, Vol.115 (Plenum Press, New York, N.Y., 1984);B. Zumino: inRelativity, Groups Topology II, Les Houches 1983, edited byB. S. de Witt andR. Stora (North Holland, Amsterdam, 1984).

    Google Scholar 

  3. For a recent review seeE. A. Bergshoeff andR. Kallosh: talk given at theTrieste Conference on Supermembranes and Physics in 2 + 1Dimensions, July 1989, CERN-TH 5566/89 preprint.

  4. I. A. Batalin andG. A. Vilkovisky:Phys. Lett. B,102, 27 (1981);Phys. Rev. D,28, 2567 (1983).

    Article  MathSciNet  ADS  Google Scholar 

  5. D. Z. Freedman andP. K. Townsend:Nucl. Phys. B,177, 282 (1980).

    Article  MathSciNet  ADS  Google Scholar 

  6. S. P. De Alwis, M. T. Grisaru andL. Mezincescu:Phys. Lett. B,190, 122 (1987);Nucl. Phys. B,303, 57 (1988).

    Article  MathSciNet  ADS  Google Scholar 

  7. W. Troost, P. van Nieuwenhuizen andA. van Proeyen:Nucl. Phys. B,333, 727 (1990).

    Article  ADS  Google Scholar 

  8. M. Henneaux:Lectures on the Antifield-BRST Formalism for Gauge Theories, ULB-TH2/89/07 preprint, to appear inProceedings of the XX GIFT Meeting (Jaca, Spain 1989), (North Holland Delta Series, Amsterdam) and inQuantum Mechanics of Fundamental Systems 3, edited byC. Teitelboim andJ. Zanelli (Plenum Press, New York, N.Y., 1989).

    Google Scholar 

  9. A. S. Schwarz:Lett. Math. Phys.,2, 247 (1978);Commun. Math. Phys.,67, 1 (1979);A. S. Schwars andY. S. Tyupkin:Nucl. Phys. B,242, 436 (1984).

    Article  ADS  MATH  Google Scholar 

  10. L. Cappiello andG. Fiore:Nuovo Cimento A,104, 899 (1991).

    Article  MathSciNet  ADS  Google Scholar 

  11. M. Blau andG. Thompson:Ann. Phys.,205, 130 (1991);Phys. Lett. B,228, 64 (1989).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. S. A. Frolov andA. A. Slavnov:Nucl. Phys. B,347, 333 (1990);A. A. Slavnov:Nucl. Phys. B (Proc. Suppl.),15, 107 (1990).

    Article  ADS  Google Scholar 

  13. E. Witten:Nucl. Phys. B,268, 253 (1986);276, 291 (1986).

    Article  ADS  Google Scholar 

  14. J. Mañes, R. Stora andB. Zumino:Commun. Math. Phys.,102, 157 (1985).

    Article  ADS  MATH  Google Scholar 

  15. V. Ogievetsky andI. V. Polubarinov:Yad. Fiz.,4, 210 (1968);S. Deser:Phys. Rev.,178, 1931 (1969);K. Hayashi:Phys. Lett. B,44, 497 (1973);M. Kalb andP. Ramond:Phys. Rev. D,9, 2273 (1974);E. Cremmer andJ. Scherk:Nucl. Phys. B,72, 117 (1974);Y. Nambu,Phys. Rep. C,23, 250 (1976).

    Google Scholar 

  16. M. Blagojević andB. Sazdović:Phys. Lett. B,223, 325 (1989).

    Article  ADS  Google Scholar 

  17. A. H. Diaz:Phys. Lett. B,203, 408 (1988).

    Article  MathSciNet  ADS  Google Scholar 

  18. L. Baulieu, E. Bergshoeff andE. Sezgin:Nucl. Phys. B,307, 348 (1988).

    Article  MathSciNet  ADS  Google Scholar 

  19. C. Battle andJ. Gomis:Phys. Rev. D,38, 1169 (1988)

    Article  ADS  Google Scholar 

  20. E. Kähler:Abh. Dt. Akad. Wiss. Ber., Kl. Math. Phys. Tech., Jahrg. 1960, Nr. 4; Jahrg. 1961, Nr. 1.

  21. I. A. Batalin:J. Math Phys.,22, 1837 (1981);I. A. Batalin andG. A. Vilkovisky,Nucl. Phys. B,234, 106 (1984).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  22. E. Witten:Commun. Math. Phys.,117, 353 (1988).

    Article  ADS  MATH  Google Scholar 

  23. J. C. Wallet:Phys. Lett. B,235, 71 (1990).

    Article  MathSciNet  ADS  Google Scholar 

  24. K. Fujikawa:Phys. Rev. D,5, 258 (1984);W. Siegel:Phys. Lett. B,149, 157, 162 (1984);151, 391, 396 (1985);W. Siegel andB. Zwiebach:Nucl. Phys. B,263, 105 (1986);T. Banks andM. Peskin:Nucl. Phys. B,264, 513 (1986);K. Itoh, T. Kugo, H. Kunitomo andH. Ooguri:Progr. Theor. Phys.,75, 162 (1986);A. Neveu, H. Nicolai andP. C. West:Phys. Lett. B,167, 307 (1986);M. Peskin andC. Thorn:Nucl. Phys. B,269, 509 (1986).

    MathSciNet  Google Scholar 

  25. M. Kato andK. Ogawa:Nucl. Phys. B,212, 443 (1983).

    Article  ADS  Google Scholar 

  26. M. Bochicchio:Phys. Lett. B,188, 330 (1987);193, 31 (1987).

    Article  MathSciNet  ADS  Google Scholar 

  27. M. Blagojević andB. Sazdović:Phys. Lett. B,223, 331 (1989).

    Article  MathSciNet  ADS  Google Scholar 

  28. C. Thorn:Nucl. Phys. B,287, 61 (1987).

    Article  MathSciNet  ADS  Google Scholar 

  29. G. T. Horowitz, J. Lykken, R. Rohm andA. Strominger:Phys. Rev. Lett.,57, 283 (1986).

    Article  MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Scienze Fisiche, Università di Napoli, Napoli

    M. Abud & L. Cappiello

  2. INFN, Sezione di Napoli, Mostra d’Oltremare, Pad. 19, I-80125, Napoli

    M. Abud & L. Cappiello

  3. Laboratoire de Physique Théorique, Université de Bordeaux I, Rue du Solarium, F-33170, Gradignan, France

    J. -P. Ader

Authors
  1. M. Abud
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  2. J. -P. Ader
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  3. L. Cappiello
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Additional information

Partially supported by INFN and MPI 60%.

Unité associeé au CNRS, UA no 764.

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Abud, M., Ader, J.P. & Cappiello, L. A BRST lagrangian quantization of reducible gauge theories: Non-abelianp-forms and string field theories. Nuov Cim A 105, 1507–1537 (1992). https://doi.org/10.1007/BF02731982

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  • DOI: https://doi.org/10.1007/BF02731982

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