×
Knizhnik, V. G.; Zamolodchikov, A. B.

Current algebras and Wess-Zumino model in two dimensions. (English) Zbl 0661.17020

Nucl. Phys. B 247, No. 1, 83-103 (1984).
We investigate quantum field theory in two dimensions invariant with respect to conformal (Virasoro) and non-abelian current (Kac-Moody) algebras. The Wess-Zumino model is related to the special case of the representations of these algebras, the conformal generators being quadratically expressed in terms of currents. The anomalous dimensions of the Wess-Zumino fields are found exactly, and the multipoint correlation functions are shown to satisfy linear differential equations. In particular, Witten’s non-abelian bosonisation rules are proven.

Cited in 12 Reviews
Cited in 364 Documents

MSC:

17B65 Infinite-dimensional Lie (super)algebras
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics

Keywords:

quantum field theory; Virasoro; Kac-Moody; Wess-Zumino model; representations
PDF BibTeX XML Cite
\textit{V. G. Knizhnik} and \textit{A. B. Zamolodchikov}, Nucl. Phys., B 247, No. 1, 83--103 (1984; Zbl 0661.17020)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] Novikov, S.P., Usp. mat. nauk, 37, 3, (1982)
[2] Witten, E., Comm. math. phys., 92, 455, (1984)
[3] Polyakov, A.M.; Wiegmann, P.B., Phys. lett., B131, 121, (1983)
[4] Polyakov, A.M.; Wiegmann, P.B., Phys. lett. B, (1984), to be published
[5] E.I. Ogievetsky, N.Yu. Reshetikhind and P.B. Wiegmann, Nucl. Phys. B, to be published
[6] Faddeev, L.D.; Reshetikhind, N.Yu., Problems of nonlinear and nonlocal quantum field theory, (1984), Dubna
[7] Polyakov, A.M., Phys. lett., 103B, 207, (1981)
[8] Di Vecchia, P.; Rossi, P., Preprint TH-3808 CERN, (1984)
[9] Belavin, A.A.; Polyakov, A.M.; Zamolodchikov, A.B., Nucl. phys., B241, 333, (1984)
[10] Dashen, R.; Frishman, Y., Phys. rev., D11, 2781, (1975)
[11] Friedan, D.; Qui, Z.; Shenker, S., Chicago preprint EFI-83-66, (1983)
[12] Kac, V.G., Infinite dimensional Lie algebras, progress in mathematics, vol. 44, (1984), Birkhäuser
[13] Polyakov, A.M., Zhetf, 66, 23, (1974)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.