Correlators of Matrix Models on Homogeneous Spaces

We investigate the correlators of TrA_{mu}A_{nu} in matrix models on homogeneous spaces: S^2 and S^2 x S^2. Their expectation value is a good order parameter to measure the geometry of the space on which non-commutative gauge theory is realized. They also serve as the Wilson lines which carry the minimum momentum. We develop an efficient procedure to calculate them through 1PI diagrams. We determine the large N scaling behavior of the correlators. The order parameter shows that fuzzy S^2 x S^2 acquires a 4 dimensional fractal structure in contrast to fuzzy S^2. We also find that the two point functions exhibit logarithmic scaling violations.