×
Dolan, L.; Goddard, P.; Montague, P.

Conformal field theories, representations and lattice constructions. (English) Zbl 0878.17025

Commun. Math. Phys. 179, No. 1, 61-120 (1996).
The authors provide the details omitted from their earlier work [Phys. Lett. B 236, 165-172 (1990)]. In this and their earlier work, the authors generalized the construction of the Monster moonshine vertex operator algebras by I. Frenkel, J. Lepowsky and A. Meurman [Vertex operator algebras and the Monster, New York, Academic Press (1988; Zbl 0674.17001)]. In their works, they use the skew symmetry of vertex operators to define intertwining operators of modules of a vertex operator algebra. Then they define certain adjoint intertwining operators by using certain Hermitian forms. Furthermore, such intertwining operators are proved to give new vertex operator algebras from a vertex operator algebra associated with an integral lattice. The “triality” (introduced by Frenkel, Lepowsky and Meurman) was deduced from certain properties of their constructed intertwining operators.
Reviewer: Xu Xiaoping (Kowloon)

Cited in 50 Documents

MSC:

17B69 Vertex operators; vertex operator algebras and related structures
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics

Keywords:

conformal field theory; triality operator; locality; vertex operator algebras; intertwining operators

Citations:

Zbl 0674.17001
Cite Review PDF
Full Text: DOI arXiv

References:

[1] Dolan, L., Goddard, P., Montague, P.: Phys. Lett.B236, 165 (1990) · doi:10.1016/0370-2693(90)90821-M
[2] Verlinde, E.: Nucl. Phys.B300, 360 (1988) · Zbl 1180.81120 · doi:10.1016/0550-3213(88)90603-7
[3] Ginsparg, P.: Applied Conformal Field Theory. Preprint HUTP-88/A054 (1988)
[4] Moore, G., Seiberg, N.: Lectures on RCFT. Preprint RU-89-32, YCTP-P13-89 (1989) · Zbl 0728.57012
[5] Frenkel, I., Lepowsky, J., Meurman, A.: Proc. Natl. Acad. Sci. USA81, 3256 (1984) · Zbl 0543.20016 · doi:10.1073/pnas.81.10.3256
[6] Frenkel, I., Lepowsky, J., Meurman, A.: In: Vertex Operators in Mathematics and Physics. Proc. 1983 MSRI Conf., Lepowsky, J. et al., (eds.) Berlin, Heidelberg, New York: Springer 1985, p. 231 · Zbl 0759.20001
[7] Frenkel, I., Lepowsky, J., Meurman: Vertex Operator Algebras and the Monster. New York: Academic Press, 1988 · Zbl 0674.17001
[8] Griess, R.: Invent. Math.69, 1 (1982) · Zbl 0498.20013 · doi:10.1007/BF01389186
[9] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups. Berlin, Heidelberg, New York: Springer 1988 · Zbl 0634.52002
[10] Conway, J.H., Curtis, R.T., Norton, S.P., Parker, R.A., Wilson, R.A.: ATLAS of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups. Oxford: Clarendon Press, 1985 · Zbl 0568.20001
[11] Dolan, L., Goddard, P., Montague, P.: Nucl. Phys.B338, 529 (1990) · doi:10.1016/0550-3213(90)90644-S
[12] Goddard, P.: Meromorphic Conformal Field Theory. In: Infinite dimensional Lie algebras and Lie groups Proceedings of the CIRM-Luminy Conference, 1988. Singapore; World Scientific, 1989, p. 556
[13] Borcherds, R.E.: Proc. Natl. Acad. Sci. USA83, 3068 (1986) · Zbl 0613.17012 · doi:10.1073/pnas.83.10.3068
[14] Frenkel, I.B., Huang, Y.-Z., Lepowsky, J.: On axiomatic approaches to vertex operator algebras and modules. Preprint (1989) · Zbl 0789.17022
[15] Goddard, P., Kent, A., Olive, D.: Phys. Lett.152B, 88 (1985); Commun. Math. Phys.103, 105 (1986)
[16] Conway, J.H., Pless, V.: Combinatorial Theory Series A28, 26 (1980) · Zbl 0439.94011 · doi:10.1016/0097-3165(80)90057-6
[17] Venkov, B.B.: Trudy Matematicheskogo Instituta imeni V.A. Steklova148, 65 (1978); Proceedings of the Steklov Institute of Mathematics4, 63 (1980)
[18] Thompson, J.G.: Bull. London Math. Soc.11, 352 (1979) · Zbl 0425.20016 · doi:10.1112/blms/11.3.352
[19] Bruce, D., Corrigan, E., Olive, D.: Nucl. Phys.B95, 427 (1975) · doi:10.1016/0550-3213(75)90326-0
[20] Hollowood, T.J.: Twisted Strings, Vertex Operators and Algebras. Durham University Ph.D. Thesis, 1988
[21] Tits, J.: Résumé de Cours, Annuaire du Collège de France 1982–198389; Invent. Math.78, 49 (1984)
[22] Goddard, P., Nahm, W., Olive, D., Schwimmer, A.: Commun. Math. Phys.107, 179 (1986) · Zbl 0602.17011 · doi:10.1007/BF01209391
[23] Montague, P.: Codes, Lattices and Conformal Field Theories. Cambridge University Ph.D. Thesis, 1992
[24] Montague, P.: On Representations of Conformal Field Theories and the Construction of Orbifolds. To appear, 1994 · Zbl 0999.81531
[25] Dong, C.: Twisted Modules for Vertex Algebras Associated with Even lattices. Santa Cruz preprint, 1992
[26] Dong, C.: Representations of the Moonshine Module Vertex Operator Algebra. Santa Cruz preprint, 1992
[27] Montague, P.: Continuous Symmetries of Lattice Conformal Field Theories and theirZ 2-Orbifolds. To appear, 1994
[28] Goddard, P.: Meromorphic Conformal Field Theory. Infinite dimensional Lie algebras and Lie groups: Proceedings of the CIRM-Luminy Conference, Singapore: World Scientific, 1989, p. 556
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.