Fuzzy Actions and their Continuum Limits

Previously matrix model actions for "fuzzy" fields have been proposed using noncommutative geometry. They retained "topological" properties extremely well, being capable of describing instantons, θ-states, the chiral anomaly, and even chiral fermions with no "doubling." Here, we demonstrate that the standard scalar and spinor actions on a d-dimensional manifold are recovered from such actions in the limit of large matrices if their normalizations are correctly scaled as the limit is taken.