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Communications in Mathematical Physics

, Volume 146, Issue 2, pp 277–309 | Cite as

Monstrous Moonshine from orbifolds

  • Michael P. Tuite
Article

Abstract

We consider the Monster Module of Frenkel, Lepowsky, and Meurman as aZ2 orbifold of a bosonic string compactified by the Leech lattice. We show that the main Conway and Norton Monstrous Moonshine properties, stating that the Thompson series for each Monster group conjugacy class has a modular invariance group of genus zero, follow from an orbifold construction based on an orbifold group composed of Monster group elements. it is shown that a conjectured vacuum structure for the orbifold twisted sectors is sufficient to specify the modular group and the genus zero property for each Thompson series. It is also shown that the Power Map formula of Conway and Norton follows from the same vacuum structure. Finally, we demonstrate the validity of the vacuum conjectures for sectors twisted by Leech lattice automorphisms in many cases.

Keywords

Quantum Computing Conjugacy Class Group Element Invariance Group Modular Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Michael P. Tuite
    • 1
  1. 1.Dublin Institute for Advanced StudiesDublin 4Ireland

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