Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-01-07
JHEP 0405 (2004) 005
Physics
High Energy Physics
High Energy Physics - Theory
Latex 37 pages, 13 figures, discussion on instabilities refined, references added, typo corrected, the final version to appear
Scientific paper
10.1088/1126-6708/2004/05/005
Fuzzy spheres appear as classical solutions in a matrix model obtained via dimensional reduction of 3-dimensional Yang-Mills theory with the Chern-Simons term. Well-defined perturbative expansion around these solutions can be formulated even for finite matrix size, and in the case of $k$ coincident fuzzy spheres it gives rise to a regularized U($k$) gauge theory on a noncommutative geometry. Here we study the matrix model nonperturbatively by Monte Carlo simulation. The system undergoes a first order phase transition as we change the coefficient ($\alpha$) of the Chern-Simons term. In the small $\alpha$ phase, the large $N$ properties of the system are qualitatively the same as in the pure Yang-Mills model ($\alpha =0$), whereas in the large $\alpha$ phase a single fuzzy sphere emerges dynamically. Various `multi fuzzy spheres' are observed as meta-stable states, and we argue in particular that the $k$ coincident fuzzy spheres cannot be realized as the true vacuum in this model even in the large $N$ limit. We also perform one-loop calculations of various observables for arbitrary $k$ including $k=1$. Comparison with our Monte Carlo data suggests that higher order corrections are suppressed in the large $N$ limit.
Azuma Takehiro
Bal Subrata
Nagao Keiichi
Nishimura Jun
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