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, theta -states, the chiral ano maly, and even chiral fermions with no "doubling." Here, we demonstrate tha t the standard scalar and spinor actions on a d-dimensional manifold are re covered from such actions in the limit of large matrices if their normaliza tions are correctly scaled as the limit is taken.