Mathieu Moonshine and symmetry surfing

Mathieu Moonshine, the observation that the Fourier coefficients of the elliptic genus on K3 can be interpreted as dimensions of representations of the Mathieu group $M_{24}$, has been proven abstractly, but a conceptual understanding in terms of a representation of the Mathieu group on the BPS states, is missing. Some time ago, Taormina and Wendland showed that such an action can be naturally defined on the lowest non-trivial BPS states, using the idea of 'symmetry surfing', i.e. by combining the symmetries of different K3 sigma models. In this paper we find non-trivial evidence that this construction can be generalized to all BPS states. (paper)