\(W\)-algebras with set of primary fields of dimensions \((3,4,5)\) and \((3,4,5,6)\). (English) Zbl 1043.81566
Summary: We show that the Jacobi-identities for a \(W\)-algebra with primary fields of dimensions 3, 4 and 5 allow two different solutions. The first solution can be identified with \(WA_4\). The second is special in the sense that, even though associative for general values of the central charge, null-fields appear that violate some of the Jacobi-identities, a fact that is usually linked to exceptional \(W\)-algebras. In contrast we find for the algebra that has an additional spin-6 field only the solution \(WA_5\).
MSC:
| 81R10 | Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations |
| 17B81 | Applications of Lie (super)algebras to physics, etc. |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
References:
| [1] | Bouwknegt, P.; Schoutens, K., Phys. Rep., 223, 183 (1993) |
| [2] | L. Frappt, E. Ragoucy and P. Sorba, W-algebras and superalgebras from constrained WZW models: A group theoretical classification, ENSLAPP-AL-391-92; L. Frappt, E. Ragoucy and P. Sorba, W-algebras and superalgebras from constrained WZW models: A group theoretical classification, ENSLAPP-AL-391-92 |
| [3] | Fehér, L.; O’Raifeartaigh, L.; Ruelle, P.; Tsutsui, I.; Wipf, A., Phys. Rep., 222, 1 (1992) |
| [4] | Bowcock, P.; Watts, G. M.T., Nucl. Phys., B379, 63 (1992) |
| [5] | Zamolodchikov, A. B., Theor. Math. Phys., 65, 347 (1986) |
| [6] | Thielemans, K., Int. J. Mod. Phys., C2, 787 (1991) · Zbl 0940.81500 |
| [7] | Wolfram, S., Mathematica (1991), Addison-Wesley: Addison-Wesley Reading, MA |
| [8] | Blumenhagen, R.; Flohr, M.; Kliem, A.; Nahm, W.; Recknagel, A.; Varnhagen, R., Nucl. Phys., B361, 255 (1991) |
| [9] | Hornfeck, K., Phys. Lett., 275B, 355 (1992) |
| [10] | Fateev, V. A.; Lukyanov, S. L., Int. J. Mod. Phys., A3, 507 (1988) |
| [11] | Pope, C. N.; Romans, L. J.; Shen, X., Nucl. Phys., 339B, 191 (1990) |
| [12] | Hull, C. M.; Palacios, L., Mod. Phys. Lett., A7, 2619 (1992) · Zbl 1021.81537 |
| [13] | Kausch, H. G.; Watts, G. M.T., Nucl. Phys., B354, 740 (1991) |
| [14] | Bouwknegt, P., Extended conformal algebras from Kac-Moody algebras in Infinite-dimensional Lie algebras and Lie groups, (Kac, V., Proc. CIRM-Luminy Conf. 1988 (1989), World Scientific: World Scientific Singapore) |
| [15] | Kausch, H. G., Chiral algebras in conformal field theory, (PhD-Thesis at the University of Cambridge (1991)) |
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