Rational Generalised Moonshine from Abelian Orbifoldings of the Moonshine Module
Ivanov, Rossen I. Tuite, Michael P.
Ivanov, Rossen I.
Tuite, Michael P.
Publication Date
2001
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journal article
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Rossen I. Ivanov and Michael P. Tuite(2001)Rational Generalised Moonshine from Abelian Orbifoldings of the Moonshine Module, Nucl.Phys. B635 (2002) 435-472
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.
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CC BY-NC-ND