Anne Taormina, Katrin Wendland
Prompted by the Mathieu Moonshine observation, we identify a pair of 45-dimensional vector spaces of states that account for the first order term in the massive sector of the elliptic genus of K3 in every $\Z_2$-orbifold CFT on K3. Remarkably, these vector spaces furnish well-defined representations of the symmetry groups that can be expected to contribute to Mathieu Moonshine. Moreover, each such representation is induced by the 45-dimensional irreducible representation of the Mathieu group M24 constructed by Margolin. We discover a new obstruction to the enhancement of representations of symmetry groups, which is due to a twist occurring in Margolin's representation. We prove that this twist can be undone in the case of $\Z_2$-orbifold CFTs on K3 for all symmetry groups that are induced from geometric symmetries of the underlying toroidal theories. We conjecture that in general, the twist can be undone if the representation yields exclusively geometric symmetries in some fixed geometric interpretation of a CFT on K3.
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http://arxiv.org/abs/1303.3221
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