Unravelling Mathieu moonshine Original Research Article

The D1–D5–KK–p system naturally provides an infinite-dimensional module graded by the dyonic charges whose dimensions are counted by the Igusa cusp form, image. We show that the Mathieu group, image, acts on this module by recovering the Siegel modular forms that count twisted dyons as a trace over this module. This is done by recovering Borcherds product formulae for these modular forms using the image action. This establishes the correspondence (‘moonshine’) proposed in that relates conjugacy classes of image to Siegel modular forms. This also, in a sense that we make precise, subsumes existing moonshines for image that relates its conjugacy classes to eta-products and Jacobi forms.