Perturbative versus nonperturbative dynamics of the fuzzy S²*S²

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We study a matrix model with a cubic term, which incorporates both the fuzzy S²*S² and the fuzzy S² as classical solutions. Both of the solutions decay into the vacuum of the pure Yang-Mills model (even in the large-N limit) when the coefficient of the cubic term is smaller than a critical value, but the large-N behavior of the critical point is different for the two solutions. The results above the critical point are nicely reproduced by the all order calculations in perturbation theory. By comparing the free energy, we find that the true vacuum is given either by the fuzzy S² or by the ``pure Yang-Mills vacuum'' depending on the coupling constant. In Monte Carlo simulation we do observe a decay of the fuzzy S²*S² into the fuzzy S² at moderate N, but the decay probability seems to be suppressed at large N. The above results, together with our previous results for the fuzzy CP², reveal certain universality in the large-N dynamics of four-dimensional fuzzy manifolds realized in a matrix model with a cubic term.