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Let be the self-dual (or holomorphic) bosonic conformal field theory associated with the spin lattice Γ of rank divisible by 24. In earlier work of the authors we showed how it is possible to establish the existence and uniqueness of irreducible-twisted sectors for, for certain automorphisms of, and to establish the modular invariance of the space of partition functions(, τ) corresponding to commuting pairs of elements in certain groups of automorphisms of. In the present work we show that if we take=24 and the sporadic simple group, then the corresponding orbifold has the. That is, each, τ) is either identically zero or a, i.e., it generates the field of functions on the subgroup of(ℝ) which fixes, τ), which then necessarily has genus zero.

An orbifold theory of genus zero associated to the sporadic groupM 24