Perturbative dynamics of fuzzy spheres at largeN

We clarify some peculiar aspects of the perturbative expansion around aclassical fuzzy-sphere solution in matrix models with a cubic term. While theeffective action in the large-N limit is saturated at the one-loop level, wefind that the ``one-loop dominance'' does not hold for generic observables dueto one-particle reducible diagrams. However, we may exploit the one-loopdominance for the effective action and obtain various observables to all ordersfrom one-loop calculation by simply shifting the center of expansion to the``quantum solution'', which extremizes the effective action. We confirm thevalidity of this method by comparison with the direct two-loop calculation andwith Monte Carlo results in the 3d Yang-Mills-Chern-Simons matrix model. Fromthe all order result we find that the perturbative expansion has a finiteradius of convergence.Comment: 21 pages, 9 figures, (v2) all order analyses added, (v3) some typos correcte