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Global gauge anomalies in coset models of conformal field theory. (English) Zbl 1292.81124
Summary: We study the occurrence of global gauge anomalies in the coset models of two-dimensional conformal field theory that are based on gauged WZW models. A complete classification of the non-anomalous theories for a wide family of gauged rigid adjoint or twisted-adjoint symmetries of WZW models is achieved with the help of Dynkin’s classification of Lie subalgebras of simple Lie algebras.

81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T50 Anomalies in quantum field theory
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
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[1] Hull, C.M.; Spence, B., The gauged nonlinear sigma model with Wess-Zumino term, Phys. Lett. B, 232, 204-210, (1989)
[2] Jack, I.; Jones, D.R.T.; Mohammedi, N.; Osborn, H., Gauging the general σ-model with a Wess-Zumino term, Nucl. Phys. B, 332, 359-379, (1990)
[3] Gawȩdzki, K.; Suszek, R.R.; Waldorf, K., Global gauge anomalies in two-dimensional bosonic sigma models, Commun. Math. Phys., 302, 513-580, (2011) · Zbl 1213.81167
[4] Gawȩdzki, K.; Suszek, R.R.; Waldorf, K., The gauging of two-dimensional bosonic sigma models on world-sheets with defects, Rev. Math. Phys., 25, 1350010, (2013) · Zbl 1278.81135
[5] Goddard, P.: Infinite dimensional Lie algebras: representations and applications. In: Frolík, Z., Souček, V., Vinárek, J. (eds.) WSGP5 Proceedings of the Winter School eometry and Physics, pp. 73-107. Circolo Matematico di Palermo, Palermo (1985) · Zbl 0593.17014
[6] Goddard, P.; Kent, A.; Olive, D., Virasoro algebras and coset space models, Phys. Lett. B, 152, 88-92, (1985) · Zbl 0661.17015
[7] Bardakci, K.; Rabinovici, E.; Säring, B., String models with \(c\) < 1 components, Nucl. Phys. B, 299, 151-182, (1988) · Zbl 0661.17018
[8] Gawȩdzki, K.; Kupiainen, A., \(G\)/\(H\) conformal field theory from gauged WZW model, Phys. Lett. B, 215, 119-123, (1988)
[9] Gawȩdzki, K.; Kupiainen, A., Coset construction from functional integral, Nucl. Phys. B, 320, 625-668, (1989)
[10] Karabali, D.; Park, Q.; Schnitzer, H.J.; Yang, Z., A GKO construction based on a path integral formulation of gauged Wess-Zumino-Witten actions, Phys. Lett. B, 216, 307-312, (1989)
[11] Dynkin, E.B.: Semisimple subalgebras of semisimple Lie algebras. Mat. Sb. (N.S.) 30(72):2, 349-462 (1952) · Zbl 0048.01701
[12] Felder, G.; Gawȩdzki, K.; Kupiainen, A., Spectra of Wess-Zumino-Witten models with arbitrary simple groups, Commun. Math. Phys., 117, 127-158, (1988) · Zbl 0642.22005
[13] Gawȩdzki, K.; Reis, N., Basic gerbe over non-simply connected compact groups, J. Geom. Phys., 50, 28-55, (2004) · Zbl 1067.22009
[14] Gawȩdzki, K.: Topological actions in two-dimensional quantum field theory. In: Hooft, G.’t, Jaffe, A., Mack, G., Mitter, P., Stora, R. (eds.) Non-perturbative Quantum Field Theory, pp. 101-142. Plenum Press, New York, London (1988)
[15] Gawȩdzki, K.; Reis, N., WZW branes and gerbes, Rev. Math. Phys., 14, 1281-1334, (2002) · Zbl 1033.81067
[16] Schellekens, A.N.; Yankielowicz, S., Simple currents, modular invariants, and fixed points, Int. J. Mod. Phys. A, 5, 2903-2952, (1990) · Zbl 0706.17012
[17] Lorente, M.; Gruber, B., Classification of semisimple subalgebras of simple Lie algebras, J. Math. Phys., 13, 1639-1663, (1972) · Zbl 0241.17006
[18] Gawȩdzki, K.; Reis, N., Abelian and non-abelian branes in WZW models and gerbes, Commun. Math. Phys., 258, 23-73, (2005) · Zbl 1094.81047
[19] Dynkin, E.B., Maximal subgroups of classical groups, Uspekhi Mat. Nauk, 7:6(52), 226-229, (1952) · Zbl 0047.02301
[20] Minchenko, A., The semisimple subalgebras of exceptional Lie algebras, Trans. Moscow Math. Soc., 67, 225-259, (2006) · Zbl 1152.17003
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