Effective Actions of Matrix Models on Homogeneous Spaces

We evaluate the effective actions of supersymmetric matrix models on fuzzy S^2times S^2 up to the two loop level. Remarkably it turns out to be a consistent solution of IIB matrix model. Based on the power counting and SUSY cancellation arguments, we can identify the t Hooft coupling and large N scaling behavior of the effective actions to all orders. In the large N limit, the quantum corrections survive except in 2 dimensional limits. They are O(N) and O(N^{4over 3}) for 4 and 6 dimensional spaces respectively. We argue that quantum effects single out 4 dimensionality among fuzzy homogeneous spaces.