Mathieu moonshine and symmetries of K3 sigma models

We review evidence for an action of the largest Mathieu group on the space of BPS states contributing to the elliptic genus of K3 (‘Mathieu moonshine’). As a first step in trying to understand this action we discuss a theorem classifying symmetries of nonlinear sigma-models on K3 which commute with the superconformal algebra. We illustrate this theorem by discussing as a particular example the sigmamodel on .