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We study renormalization in a scalar field theory on the fuzzy sphere. Thetheory is realized by a matrix model, where the matrix size plays the role of aUV cutoff. We define correlation functions by using the Berezin symbolidentified with a field and calculate them nonperturbatively by Monte Carlosimulation. We find that the 2-point and 4-point functions are made independentof the matrix size by tuning a parameter and performing a wave functionrenormalization. The results strongly suggest that the theory isnonperturbatively renormalizable in the ordinary sense.

Correlation functions and renormalization in a scalar field theory on the fuzzy sphere