Perturbative dynamics of fuzzy spheres at large N

We clarify some peculiar aspects of the perturbative expansion around a classical fuzzy-sphere solution in matrix models with a cubic term. While the effective action in the large-N limit is saturated at the one-loop level, we find that the “one-loop dominance” does not hold for generic observables due to one-particle reducible diagrams. However, we may exploit the one-loop dominance for the effective action and obtain various observables to all orders from one-loop calculation by simply shifting the center of expansion to the “quantum solution”, which extremizes the effective action. We confirm the validity of this method by comparison with the direct two-loop calculation and with Monte Carlo results in the 3d Yang-Mills-Chern-Simons matrix model. From the all order result we find that the perturbative expansion has a finite radius of convergence.