Higher spin gauge theory on fuzzy SN4

We examine in detail the higher spin fields which arise on the basic fuzzy sphere S-N(4) in the semi-classical limit. The space of functions can be identified with functions on classical S-4 taking values in a higher spin algebra associated to so(5). We derive an explicit and complete classification of the scalars and one-forms on the semi-classical limit of S-N(4). The resulting kinematics is reminiscent of Vasiliev theory. Yang-Mills matrix models naturally provide an action formulation for higher spin gauge theory on S-4, with four irreducible modes for each spin s >= 1. We diagonalize the quadratic part of the effective action and exactly evaluate the quadratic part in the spin 2 sector. By identifying the linear perturbation of the effective metric, we obtain the exact kinetic term for all graviton candidates. At the classical level, matter T-mu nu 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 T-mu nu. The latter is too large to be physically acceptable, unless there is a significant induced quantum action. This issue should be resolved on generalized fuzzy spaces.