The author wishes to thank Bobby Acharya, Mark Haskins and Johannes Nordström for an inspiring conversation at the Mathematisches Forschungsinstitut Oberwolfach in February 2015 which was the original inspiration for this work. He also wishes to thank Mark Haskins for reading an earlier version of the paper and for many discussions and suggestions for improvement. Discussions with Mark Haskins on this work and related topics were also made possible thanks to the support of his EPSRC grant EP/L001527/1, “Singular spaces of special and exceptional holonomy”. The paper is based on work supported by the National Science Foundation under Grant No. DMS-1440140 while the author was in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Spring 2016 semester.