Fuchs, Jürgen Simple WZW currents. (English) Zbl 0736.17033 Commun. Math. Phys. 136, No. 2, 345-356 (1991). Summary: A complete classification of simple currents of WZW theories is obtained. The proof is based on an analysis of the quantum dimensions of the primary fields. Simple currents are precisely the primaries with unit quantum dimension; for WZW theories explicit formulae for the quantum dimensions can be derived so that an identification of the fields with unit quantum dimension is possible. Cited in 28 Documents MSC: 17B81 Applications of Lie (super)algebras to physics, etc. Keywords:quantum dimensions; Wess-Zumino-Witten models; conformal field theories PDFBibTeX XMLCite \textit{J. Fuchs}, Commun. Math. Phys. 136, No. 2, 345--356 (1991; Zbl 0736.17033) Full Text: DOI References: [1] Schellekens, A. N., Yankielowicz, S.: Nucl. Phys.B327, 673 (1989); Nucl. Phys.B334, 67 (1990) · doi:10.1016/0550-3213(89)90310-6 [2] Knizhnik, V., Zamolodchikov, A.: Nucl. Phys.B247, 83 (1984) · Zbl 0661.17020 · doi:10.1016/0550-3213(84)90374-2 [3] Gepner, D., Witten, E.: Nucl. Phys.B278, 493 (1986) · doi:10.1016/0550-3213(86)90051-9 [4] Fuchs, J., Gepner, D.: Nucl. Phys.B294, 30 (1987) · doi:10.1016/0550-3213(87)90571-2 [5] Forgacs, P., Horváth, Z., Palla, L., Vecsernyés, P.: Nucl. Phys.B308, 477 (1988) · doi:10.1016/0550-3213(88)90574-3 [6] Verlinde, E.: Nucl. Phys.B300, 360 (1988) · Zbl 1180.81120 · doi:10.1016/0550-3213(88)90603-7 [7] Moore, G., Seiberg, N.: Phys. Lett.B212, 451 (1988) · doi:10.1016/0370-2693(88)91796-0 [8] Dijkgraaf, R., Verlinde, E.: Nucl. Phys. B. (Proc. Suppl.)5, 87 (1988) · Zbl 0958.81510 · doi:10.1016/0920-5632(88)90371-4 [9] Kac, V. G., Peterson, D. H.: Adv. Math.53, 125 (1984) · Zbl 0584.17007 · doi:10.1016/0001-8708(84)90032-X [10] Kac, V. G., M. Wakimoto: Adv. Math.70, 156 (1988) · Zbl 0661.17016 · doi:10.1016/0001-8708(88)90055-2 [11] Furlan, P., Ganchev, A. Ch., Petkova, V. P.: Nucl. Phys.B343, 205 (1990) · doi:10.1016/0550-3213(90)90601-9 [12] Fuchs, J., van Driel, P.: Nucl. Phys.B346, 632 (1990) · doi:10.1016/0550-3213(90)90296-P [13] Pasquier, V., Saleur, H.: Nucl. Phys.B330, 523 (1990) · doi:10.1016/0550-3213(90)90122-T [14] Alvarez-Gaumé, L., Gomez, C., Sierra, G.: Nucl. Phys.B330, 347 (1990) · Zbl 0764.17021 · doi:10.1016/0550-3213(90)90116-U [15] Fuchs, J., van Driel, P.: J. Math. Phys.31, 1770 (1990) · Zbl 0731.22017 · doi:10.1063/1.528673 [16] Fredenhagen, K., Rehren, K. H., Schroer, B.: Commun. Math. Phys.125, 201 (1989) · Zbl 0682.46051 · doi:10.1007/BF01217906 [17] Gepner, D.: Phys. Lett.B222, 207 (1989); Moore, G., Seiberg, N.: Phys. Lett.B220, 422 (1989); Lerche, W., Vafa, C., Warner, N.: Nucl. Phys.B324, 427 (1989) · doi:10.1016/0370-2693(89)91253-7 [18] Schellekens, A. N., Yankielowicz, S.: Int. J. Mod. Phys.A5, 2903 (1990) · Zbl 0706.17012 · doi:10.1142/S0217751X90001367 [19] Ahn, C., Walton, M.: Phys. Rev.D41, 2558 (1990) · doi:10.1103/PhysRevD.41.2558 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.