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arXiv · hep-th/0401038

Nonperturbative studies of fuzzy spheres in a matrix model with the Chern-Simons term

Takehiro Azuma·Subrata Bal·Keiichi Nagao·Jun Nishimura
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Abstract

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 ($α$) of the Chern-Simons term. In the small $α$ phase, the large $N$ properties of the system are qualitatively the same as in the pure Yang-Mills model ($α=0$), whereas in the large $α$ 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.

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Takehiro Azuma, Subrata Bal, Keiichi Nagao, Jun Nishimura. 2004-05-19. Nonperturbative studies of fuzzy spheres in a matrix model with the Chern-Simons term. https://doi.org/10.1088/1126-6708%2F2004%2F05%2F005

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