On matrix model formulations of noncommutative Yang-Mills theories

Abstract

We study the stability of noncommutative spaces in matrix models and discuss the continuum limit which leads to the noncommutative Yang-Mills theories. It turns out that most noncommutative spaces in bosonic models are unstable. This indicates perturbative instability of fuzzy ℝ𝐷 pointed out by Van Raamsdonk and Armoni et al. persists to nonperturbative level in these cases. In this sense, these bosonic noncommutative Yang-Mills theories are not well-defined, or at least their matrix model formulations studied in this paper do not work. We also show that noncommutative backgrounds are stable in a supersymmetric matrix model deformed by a cubic Myers term, though the deformation itself breaks supersymmetry.