×

zbMATH — the first resource for mathematics

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.

MSC:
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
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[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
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.