Document Type
Article
Rights
This item is available under a Creative Commons License for non-commercial use only
Disciplines
Pure mathematics, Applied mathematics
Abstract
We consider orbifoldings of the Moonshine Module with respect to the abelian group generated by a pair of commuting Monster group elements with one of prime order p = 2, 3, 5, 7 and the other of order pk for k = 1 or k prime. We show that constraints arising from meromorphic orbifold conformal field theory allow us to demonstrate that each orbifold partition function with rational coefficients is either constant or is a hauptmodul for an explicitly found modular fixing group of genus zero. We thus confirm in the cases considered the Generalised Moonshine conjectures for all rational modular functions for the Monster centralisers related to the Baby Monster, Fischer, Harada-Norton and Held sporadic simple groups. We also derive non-trivial constraints on the possible Monster conjugacy classes to which the elements of the orbifolding abelian group may belong.
DOI
https://doi.org/10.1016/S0550-3213(02)00318-8
Recommended Citation
Ivanov, R. & Tuite, M.P. (2002). Rational Generalized Moonshine from Abelian Orbifoldings of the Moonshine Module. Nuclear Physics B, vol. 635, no. 3, pg. 435-472. doi:10.1016/S0550-3213(02)00318-8
Funder
SFI
Included in
Algebra Commons, Elementary Particles and Fields and String Theory Commons, Quantum Physics Commons