×
Felder, G.; Gawȩdzki, K.; Kupiainen, A.

Spectra of Wess-Zumino-Witten models with arbitrary simple groups. (English) Zbl 0642.22005

Commun. Math. Phys. 117, No. 1, 127-158 (1988).
This is a geometrical study of two dimensional field theoretical models with fields taking their values in a Lie group (Wess-Zumino-Witten models). The authors extend their previous study in the case of SU(2) or SO(3) to an arbitrary simple group and give an explicit construction of highest weight states and modular invariant partition functions on tori.
Reviewer: C.Itzykson

Cited in 1 Review
Cited in 57 Documents

MSC:

22E70 Applications of Lie groups to the sciences; explicit representations
58Z05 Applications of global analysis to the sciences
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations

Keywords:

field theoretical models; Lie group; Wess-Zumino-Witten models; highest weight states; modular invariant partition functions
Cite Review PDF
Full Text: DOI

References:

[1] Abouelsaood, A., Gepner, D.: Phys. Lett. B176, 380-386 (1986)
[2] Bernard, D.: Nucl. Phys.B288, 628-648 (1987) · doi:10.1016/0550-3213(87)90231-8
[3] Bott, R.: Bull. Soc. Math. France84, 251-281 (1956)
[4] Bouwknegt, P., Nahm, W.: Phys. Lett.B184, 359-362 (1987)
[5] Callan, C. G., Dashen, R. F., Gross, D. J.: Phys. Lett.63B, 334 (1976)
[6] Cappelli, A., Itzykson, C., Zuber, J.-B.: The A-D-E classification of minimal andA (1) 1 conformal invariant theories. Commun. Math. Phys.113, 1-26 (1987) · Zbl 0639.17008 · doi:10.1007/BF01221394
[7] Felder, G., Gawedzki, K., Kupiainen, A.: The spectrum of Wess-Zumino-Witten models, to appear in Nucl. Phys. B
[8] Fröhlich, J.: Lectures at Cargèse Summer School, 1987
[9] Gawedzki, K.: Topological actions in two-dimensional quantum field theories, IHES preprint, 1987
[10] Gepner, D.: Nucl. Phys.B287, 111-130 (1987) · doi:10.1016/0550-3213(87)90098-8
[11] Gepner, D., Witten, E.: Nucl. Phys.B278, 493-549 (1986) · doi:10.1016/0550-3213(86)90051-9
[12] Jackiw, R., Rebbi, C.: Phys. Rev. Lett.37, 172 (1976) · doi:10.1103/PhysRevLett.37.172
[13] Kac, V. G.: Infinite dimensional Lie algebras. Cambridge: Cambridge University Press 1985 · Zbl 0574.17010
[14] Kac, V. G., Peterson, D. H.: In Arithmetics and geometry, Vol. 2, pp. 141-166. Boston: Birkhäuser 1983
[15] Knizhnik, V., Zamolodchikov, A. B.: Nucl. Phys.B247, 83-103 (1984) · Zbl 0661.17020 · doi:10.1016/0550-3213(84)90374-2
[16] Kodaira, K.: Complex manifolds and deformation of complex structures, Berlin, Heidelberg, New York: Springer 1986 · Zbl 0581.32012
[17] Kostant, B.: In: Lectures Notes in Mathematics, Vol.170, pp. 87-208. Berlin, Heidelberg, New York: Springer 1970
[18] Mac Lane, S.: Homology. Berlin, Heidelberg, New York: Springer 1963
[19] Maurin, K.: General eigenfunctions expansions and unitary representations of topological groups, PWN, Warsaw, 1968 · Zbl 0185.39001
[20] Mickelsson, J.: Commun. Math. Phys.110, 173-184 (1987) · Zbl 0625.58043 · doi:10.1007/BF01207361
[21] Olive, D. I., Goddard, P.: Lectures at Srni Winter School, 1985
[22] Polyakov, A. M., Wiegmann, P. B.: Phys. Lett.B141, 223-228 (1984)
[23] Pressley, A., Segal, G.: Loop groups. Oxford: Clarendon Press 1986 · Zbl 0618.22011
[24] Ramadas, T. R.: Commun. Math. Phys.93, 355-365 (1984) · Zbl 0569.58017 · doi:10.1007/BF01258534
[25] Séminaire, H., Cartan, Exposés 1{\(\deg\)}?4{\(\deg\)}, ENS, 1950/1951
[26] Simms, D. J., Woodhouse, N. M. J.: Lecture Notes in Physics, Vol.53, Berlin, Heidelberg, New York: Springer 1976
[27] Witten, E.: Commun. Math. Phys.92, 455-472 (1984) · Zbl 0536.58012 · doi:10.1007/BF01215276
[28] Wudka, J.: Nucl. Phys.B288, 649-658 (1987) · doi:10.1016/0550-3213(87)90232-X
[29] Zamolodchikov, A. B., Fateev, V. A.: Sov. Phys. JETP62, 215-225 (1985)
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.