Perturbative versus nonperturbative dynamics of the fuzzy S2× S2

We study a matrix model with a cubic term, which incorporates both the fuzzyS^2*S^2 and the fuzzy S^2 as classical solutions. Both of the solutions decayinto the vacuum of the pure Yang-Mills model (even in the large-N limit) whenthe coefficient of the cubic term is smaller than a critical value, but thelarge-N behavior of the critical point is different for the two solutions. Theresults above the critical point are nicely reproduced by the all ordercalculations in perturbation theory. By comparing the free energy, we find thatthe true vacuum is given either by the fuzzy S^2 or by the ``pure Yang-Millsvacuum'' depending on the coupling constant. In Monte Carlo simulation we doobserve a decay of the fuzzy S^2*S^2 into the fuzzy S^2 at moderate N, but thedecay probability seems to be suppressed at large N. The above results,together with our previous results for the fuzzy CP^2, reveal certainuniversality in the large-N dynamics of four-dimensional fuzzy manifoldsrealized in a matrix model with a cubic term.Comment: 20 pages, 7 figures, (v2) some typos correcte