Higher spin gauge theory on fuzzy S4N

2017, July 4
Marcus Sperling and Harold C. Steinacker
arXiv preprint

We examine in detail the higher spin fields which arise on the basic fuzzy sphere S4N in the semi-classical limit. The space of functions can be identified with functions on classical S4 taking values in a higher spin algebra associated to (5). Yang-Mills matrix models naturally provide an action formulation for higher spin gauge theory on S4, with 4 irreducible modes for each spin s1. At the classical level, matter Tμν leads to three different contributions to the linearized metric: one consistent with linearized GR, one more rapidly decreasing contribution, and one non-propagating contribution localized at Tμν. The latter is too large to be physically acceptable, unless there is a significant induced quantum action. This issue should be resolved on the generalized fuzzy sphere, where additional modes with suitable properties arise.