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Generalised Moonshine and Abelian Orbifold Constructions

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Show simple item record Tuite, Michael P. 2012-01-09T13:24:28Z 2012-01-09T13:24:28Z 1994
dc.identifier.citation Michael P. Tuite(1994)Generalised Moonshine and Abelian Orbifold Constructions, Michael P. Tuite en_US
dc.description.abstract We consider the application of Abelian orbifold constructions in Meromorphic Conformal Field Theory (MCFT) towards an understanding of various aspects of Monstrous Moonshine and Generalised Moonshine. We review some of the basic concepts in MCFT and Abelian orbifold constructions of MCFTs and summarise some of the relevant physics lore surrounding such constructions including aspects of the modular group, the fusion algebra and the notion of a self-dual MCFT. The FLM Moonshine Module, $V^\natural$, is historically the first example of such a construction being a $Z_2$ orbifolding of the Leech lattice MCFT, $V^\Lambda$. We review the usefulness of these ideas in understanding Monstrous Moonshine, the genus zero property for Thompson series which we have shown is equivalent to the property that the only meromorphic $Z_n$ orbifoldings of $V^\natural$ are $V^\Lambda$ and $V^\natural$ itself (assuming that $V^\natural$ is uniquely determined by its characteristic function $J(\tau)$. We show that these constraints on the possible $Z_n$ orbifoldings of $V^\natural$ are also sufficient to demonstrate the genus zero property for Generalised Moonshine functions in the simplest non-trivial prime cases by considering $Z_p\times Z_p$ orbifoldings of $V^\natural$. Thus Monstrous Moonshine implies Generalised Moonshine in these cases.
dc.format application/pdf en_US
dc.language.iso en en_US
dc.subject High Energy Physics - Theory
dc.subject Mathematics - Quantum Algebra
dc.title Generalised Moonshine and Abelian Orbifold Constructions en_US
dc.type Article en_US
dc.local.publishedsource en_US
dc.description.peer-reviewed peer-reviewed en_US
dc.local.authors Michael P. Tuite
dc.local.arxivid hep-th/9412036

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