Nonperturbative studies of fuzzy spheres in a matrix model with the ChernSimons term
Abstract
Fuzzy spheres appear as classical solutions in a matrix model obtained via dimensional reduction of 3dimensional YangMills theory with the ChernSimons term. Welldefined 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 ChernSimons term. In the small alpha phase, the large N properties of the system are qualitatively the same as in the pure YangMills model (alpha = 0), whereas in the large alpha phase a single fuzzy sphere emerges dynamically. Various `multi fuzzy spheres' are observed as metastable 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 oneloop 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.
 Publication:

Journal of High Energy Physics
 Pub Date:
 May 2004
 DOI:
 10.1088/11266708/2004/05/005
 arXiv:
 arXiv:hepth/0401038
 Bibcode:
 2004JHEP...05..005A
 Keywords:

 Nonperturbative Effects NonCommutative Geometry Matrix Models;
 High Energy Physics  Theory;
 High Energy Physics  Lattice
 EPrint:
 Latex 37 pages, 13 figures, discussion on instabilities refined, references added, typo corrected, the final version to appear in JHEP