Fuzzy Actions and their Continuum Limits

Previously matrix model actions for fuzzy'' fields have been proposed using non-commutative geometry. They retained topological’’ properties extremely well, being capable of describing instantons, $\theta$–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.