×

The supersymmetry index and the construction of modular invariants. (English) Zbl 0712.17021

Let G be a rank \(\ell\) semisimple Lie group whose Lie algebra is used to construct a Kac-Moody algebra [V. G. Kac, Infinite dimensional Lie algebras (1985; Zbl 0574.17010)]. An identity derived in a previous paper for any supersymmetric coset model [W. Lerche, C. Vafa, and the author, Nucl. Phys. B 324, 427-474 (1989)] is applied here in order to study the modular properties of affine G-characters via the modular properties of the affine characters of rank \(\ell\) semisimple subgroups of G (except possibly for U(1) factors). Applications of this relationship are then given; in particular, an algorithm for generating modular invariant combinations of affine G-characters and a way to classify modular invariants of affine G-representations.
Reviewer: U.Cattaneo

MSC:

17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Kazama, Y., Suzuki, H.: Nucl. Phys.B321, 232 (1989) · doi:10.1016/0550-3213(89)90250-2
[2] Lerche, W., Vafa, C., Warner, N.P.: Nucl. Phys.B324, 427 (1989) · doi:10.1016/0550-3213(89)90474-4
[3] Nahm, W.: Duke Math. J.54, 579 (1987) · Zbl 0631.58042 · doi:10.1215/S0012-7094-87-05424-X
[4] Davis, U.C.: Preprints (1988)
[5] Bouwknegt, P., Nahm, W.: Phys. Lett.188 B, 349 (1987)
[6] Walton, M.A.: Nucl. Phys.B 322, 775 (1989) · doi:10.1016/0550-3213(89)90237-X
[7] Schellekens, A.N., Warner, N.P.: Nucl. Phys.B 308, 397 (1988) · doi:10.1016/0550-3213(88)90570-6
[8] Lüst, D., Theisen, S.: Preprint MPI-PAE/PTh 83/87
[9] Lerche, W., Schellekens, A.N., Warner, N.P.: Phys. Rep.177, 1 (1989) · Zbl 0942.53510 · doi:10.1016/0370-1573(89)90077-X
[10] Kac, V.G.: Infinite dimensional Lie algebras, second ed. Cambridge: Cambridge University Press 1985 · Zbl 0574.17010
[11] Gepner, D., Witten, E.: Nucl. Phys.B278, 493 (1986) · doi:10.1016/0550-3213(86)90051-9
[12] Goddard, P., Olive, D.: Nucl. Phys.B257, 266 (1985) · Zbl 0661.17014 · doi:10.1016/0550-3213(85)90344-X
[13] Goddard, P., Kent, A., Olive, D.: Phys. Lett.152B, 88 (1985)
[14] Capelli, A., Itzykson, C., Zuber, J.B.: Nucl. PhysB 280, 445, (1987); Commun. Math. Phys.113, 1 (1987) · Zbl 0661.17017 · doi:10.1016/0550-3213(87)90155-6
[15] Englert, F., Neveu, A.: Phys. Lett.163 B, 349 (1985)
[16] Vafa, C.: Nucl. Phys.B273, 592 (1986) · Zbl 0992.81515 · doi:10.1016/0550-3213(86)90379-2
[17] Ginsparg, P.: Nucl. Phys.B295, 153 (1988) · doi:10.1016/0550-3213(88)90249-0
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.