Dynamical aspects of the fuzzy CP2in the largeNreduced model with a cubic term

``Fuzzy CP^2'', which is a four-dimensional fuzzy manifold extension of thewell-known fuzzy analogous to the fuzzy 2-sphere (S^2), appears as a classicalsolution in the dimensionally reduced 8d Yang-Mills model with a cubic terminvolving the structure constant of the SU(3) Lie algebra. Although the fuzzyS^2, which is also a classical solution of the same model, has actually smallerfree energy than the fuzzy CP^2, Monte Carlo simulation shows that the fuzzyCP^2 is stable even nonperturbatively due to the suppression of tunnelingeffects at large N as far as the coefficient of the cubic term ($\alpha$) issufficiently large. As \alpha is decreased, both the fuzzy CP$^2$ and the fuzzyS^2 collapse to a solid ball and the system is essentially described by thepure Yang-Mills model (\alpha = 0). The corresponding transitions are of firstorder and the critical points can be understood analytically. The gauge groupgenerated dynamically above the critical point turns out to be of rank one forboth CP^2 and S^2 cases. Above the critical point, we also perform perturbativecalculations for various quantities to all orders, taking advantage of theone-loop saturation of the effective action in the large-N limit. Byextrapolating our Monte Carlo results to N=\infty, we find excellent agreementwith the all order results.Comment: 27 pages, 7 figures, (v2) References added (v3) all order analyses added, some typos correcte