2005/06/30 by Takehiro Azuma, Subrata Bal, Keiichi Nagao +1
Physics and Astronomy · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Particle physics theoretical and experimental studies #hep-lat #hep-th
paper · pdf · doi:10.1088/1126-6708/2005/09/047
published as JHEP 0509 (2005) 047 · 20 pages, 7 figures, (v2) some typos corrected
arxiv created 2005/07/28 · openalex publication_date 2005/09/21 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.