Effective actions of matrix models on homogeneous spaces

We evaluate the effective actions of supersymmetric matrix models on fuzzy S-2 x 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-4/3) for 4- and 6-dimensional spaces, respectively. We argue that quantum effects single out 4 dimensionality among fuzzy homogeneous spaces. (C) 2003 Elsevier B.V. All rights reserved.