Renormalization on the fuzzy sphere

We study renormalization on the fuzzy sphere. We numerically simulate a scalar field theory on it, which is described by a Hermitian matrix model. We show that correlation functions defined by using the Berezin symbol are made independent of the matrix size, which is viewed as a UV cutoff, by tuning a parameter of the theory. We also find that the theories on the phase boundary are universal. They behave as a conformal field theory at short distances, while they show an effect of UV/IR mixing at long distances.