nLab Monster vertex operator algebra

Idea

The Monster vertex algebra is a super vertex operator algebra whose group of automorphisms of a super VOA is the monster group. (Frenkel-Lepowski-Meurman 89, Griess-Lam 11).

Related entries

• Moonshine

References

• Richard Borcherds, Vertex algebras, Kac-Moody algebras, and the Monster, PNAS May 1, 1986 83 (10) 3068-3071 (doi:10.1073/pnas.83.10.3068, pdf)

• Lance Dixon, Paul Ginsparg, Jeffrey Harvey, Beauty and the Beast: Superconformal Symmetry in a Monster Module, Commun, Math. Phys. 119, 221-241 (1988) (euclid:1104162400, doi:10.1007/BF01217740, pdf)

• Igor Frenkel, James Lepowsky, Arne Meurman, Vertex operator algebras and the monster, Pure and Applied Mathematics 134, Academic Press, New York 1989. liv+508 pp. MR0996026

• Richard Borcherds,John Conway, L. Queen, N. J. A. Sloane, A Monster Lie Algebra?, In: Sphere Packings, Lattices and Groups, Grundlehren der mathematischen Wissenschaften (A Series of Comprehensive Studies in Mathematics), vol 290. Springer 1993 (doi:10.1007/978-1-4757-2249-9_30, pdf)

• Robert Griess Jr., Ching Hung Lam, A new existence proof of the Monster by VOA theory (arXiv:1103.1414)

• Lisa Carbone, Elizabeth Jurisich, Scott H. Murray, Constructing a Lie group analog for the Monster Lie algebra (arXiv:2002.06658)

See also

• Wikipedia, Monster vertex algebra

• Wikipedia, Monster Lie algebra

Relation to quantum error correction:

• Jeffrey A. Harvey, Gregory W. Moore, Moonshine, Superconformal Symmetry, and Quantum Error Correction, J. High Energ. Phys. 2020, 146 (2020). (arXiv:2003.13700)

Possible relation to bosonic M-theory:

• Alessio Marrani, Michael Rios, David Chester, Monstrous M-theory (arXiv:2008.06742)

Discussion in terms of conformal nets:

• Sebastiano Carpi, Tiziano Gaudio, Robin Hillier, From vertex operator superalgebras to graded-local conformal nets and back [arXiv:2304.14263]