Mathieu Moonshine and symmetry surfing
Abstract
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 \newcommand{\m}μ \newcommand{\n}ν \newcommand{\mg}{{{M}_{24}}} \mg , 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 nontrivial BPS states, using the idea of ‘symmetry surfing’, i.e. by combining the symmetries of different K3 sigma models. In this paper we find nontrivial evidence that this construction can be generalized to all BPS states.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 November 2017
 DOI:
 10.1088/17518121/aa915f
 arXiv:
 arXiv:1609.09302
 Bibcode:
 2017JPhA...50U4002G
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Number Theory;
 Mathematics  Representation Theory
 EPrint:
 32 pages. V2: added more detailed argument on which states get lifted under symmetry surfing