A twist in the M24 moonshine story

Understand

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 Z2-orbifold CFT on K3.

• These generic states are uniquely characterized by the fact that the action of every geometric symmetry group of a Z2-orbifold CFT yields a well-defined faithful representation on them.
• Moreover, each such representation is obtained by restriction of the 45-dimensional irreducible representation of the Mathieu group M24 constructed by Margolin.
• Thus we provide a piece of evidence for Mathieu Moonshine explicitly from SCFTs on K3.