Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-06-24
JHEP 0509 (2005) 047
Physics
High Energy Physics
High Energy Physics - Theory
20 pages, 7 figures, (v2) some typos corrected
Scientific paper
10.1088/1126-6708/2005/09/047
We study a matrix model with a cubic term, which incorporates both the fuzzy S^2*S^2 and the fuzzy S^2 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 S^2 or by the ``pure Yang-Mills vacuum'' depending on the coupling constant. In Monte Carlo simulation we do observe a decay of the fuzzy S^2*S^2 into the fuzzy S^2 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 CP^2, reveal certain universality in the large-N dynamics of four-dimensional fuzzy manifolds realized in a matrix model with a cubic term.
Azuma Takehiro
Bal Subrata
Nagao Keiichi
Nishimura Jun
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