Skip to main content
Log in

Anomalies from the Wess-Zumino-Witten action

  • Published:
Zeitschrift für Physik C Particles and Fields

Abstract

We show that the two most frequent expressions for the anomalous commutators can be both derived from quantities associated with the WZW model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. S.B. Treiman, R. Jackiw, B. Zumino, E. Witten (eds.): Current algebra and anomalies. Singapore: World Scientific 1985

    Google Scholar 

  2. R. Stora: Algebraic structure and topological origin of anomalies; in: Progress in gauge field theory G. 'tHooft (ed.) New York: Plenum 1964; Algebraic structure of chiral anomaies; in: New perspectives in quantum field theories. J. Abad, M. Asorey, A. Cruz (eds.) Singapore: World Scientific 1986

    Google Scholar 

  3. B. Zumino, Y.-Shi Wu, A Zee: Nucl. Phys. B239 (1984) 477

    Google Scholar 

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

    Google Scholar 

  5. B. Zumino: Nucl. Phys. B253 (1985) 477

    Google Scholar 

  6. R. Jackiw: Topological investigations in quantized gauge theories, Ref. 1; Chern-Simons terms and cocycles in physics and mathematics; in: Models of field theory, vol. 2, I.A. Batalin, C.J. Isham, G.A. Vilkovisky (eds.) Bristol: Adam Hilger 1987

    Google Scholar 

  7. L.D. Faddeev: Phys. Lett. B145 (1984) 81

    Google Scholar 

  8. L. Álvarez-Gaumé, P. Nelson: Common. Math. Phys. 99 (1985) 103

    Google Scholar 

  9. K. Fujikawa: Phys. Lett. B171 (1986) 424

    Google Scholar 

  10. L.D. Faddeev, S.L. Shatashvili: Theor. Math. Phys. 60 (1985) 770 (Theor. i Mat. Fiz. 60 (1984) 206)

    Google Scholar 

  11. B. Zumino: Chiral anomalies and differential geometry. Ref. 1

  12. T. Fujiwara, S. Kitakado, T. Nanoyama: Phys. Lett. B155 (1985) 91

    Google Scholar 

  13. S. Jo: Nucl. Phys. B259 (1985) 616; Phys. Lett. B163 (1985) 353

    Google Scholar 

  14. M. Kobayashi, K. Seo, A. Sugamoto: Nucl. Phys. B273 (1986) 607

    Google Scholar 

  15. A. Yu. Alekseev, Ya. Madaichik, L.D. Faddeev, S.L. Shatashvili: Theor. Math. Phys. 73 (1988) 1149

    Google Scholar 

  16. F.S. Otto, H.J. Rothe, K.D. Rothe: Phys. Lett. B231 (1989) 299

    Google Scholar 

  17. Y.-Z. Zhang: Phys. Rev. Lett. 62 (1989) 2221

    Google Scholar 

  18. C. Schwiebert: Phys. Lett. B241 (1990) 223

    Google Scholar 

  19. L.D. Faddeev, S.L. Shatashvili: Phys. Lett. B 167 (1986) 225

    Google Scholar 

  20. H. Sonoda: Phys. Lett. B156 (1985) 220; Nucl. Phys. B266 (1986) 410; see also A.J. Niemi, G.W. Semenoff: Phys. Rev. Lett. 55 (1985) 927

    Google Scholar 

  21. R. Percacci, R. Rajarman: Phys. Lett. B201 (1988) 256; Int. J. Mod. Phys. A4 (1986) 4177

    Google Scholar 

  22. R. Floreanini, R. Percacci: Int. J. Mod. Phys. A4 (1989) 4581

    Google Scholar 

  23. J. Wess, B. Zumino: Phys. Lett. B37 (1977) 95 J. Wess: Acta Phys. Austr. Suppl. IX (1972) 494

    Google Scholar 

  24. E. Witten: Nucl. Phys. B223 (1983) 422; Commun. Math. Phys. 92 (1984) 455

    Google Scholar 

  25. L.D. Faddeev: in: Superstrings, anomalies and supergravity; G.W. Gibbons et al. (eds.) Cambridge: Cambridge Univ. Press 1986

    Google Scholar 

  26. R. Hermann: Infinite dimensional Lie algebras and current algebra; in: Lecture Notes in Physics 6. Berlin, Heidelberg, New York: Springer 1970; J. Math. Phys. 11 (1970) 1825

    Google Scholar 

  27. J.A. de Azcárraga, J.M. Izquierdo, A.J. Macfarlane: Ann. Phys. (N.Y.), 202 (1990) 1

    Google Scholar 

  28. C. Chevalley, S. Eilenberg: Trans. Am. Math. Soc. 63 (1948) 85

    Google Scholar 

  29. Bott, R. Seely: Commun. Math. Phys. 62 (1975) 235

    Google Scholar 

  30. S.J. Rajeev: Phys. Rev. D29 (1984) 2944

    Google Scholar 

  31. T. Fujiwara: Phys. Lett. B152 (1985) 103

    Google Scholar 

  32. (added in proof) G. Kramer, K. Meetz: Z. Phys. C—Particles and Fields 30 (1986) 317

    Google Scholar 

  33. K. Fujikawa: Phys. Rev. D21 (1980) 2848

    Google Scholar 

  34. I. Tsutsui: Phys. Lett. B229 (1989) 51

    Google Scholar 

  35. Y.-Z. Zhang: Phys. Lett. B219 (1989) 439

    Google Scholar 

  36. M. Abud, J.-P. Ader, F. Gieres: Nucl. Phys. B339 (1990) 687

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Work partially supported by CICYT (Spain) under grant # AEN90-0039

Rights and permissions

Reprints and permissions

About this article

Cite this article

de Azcárraga, J.A., Izquierdo, J.M. Anomalies from the Wess-Zumino-Witten action. Z. Phys. C - Particles and Fields 49, 627–632 (1991). https://doi.org/10.1007/BF01483579

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01483579

Keywords

Navigation