Absence of a fuzzy S4 phase in the dimensionally reduced 5d Yang-Mills-Chern-Simons model
Abstract
We perform nonperturbative studies of the dimensionally reduced 5d Yang-Mills-Chern-Simons model, in which a four-dimensional fuzzy manifold, ``fuzzy S4'', is known to exist as a classical solution. Although the action is unbounded from below, Monte Carlo simulations provide an evidence for a well-defined vacuum, which stabilizes at large N, when the coefficient of the Chern-Simons term is sufficiently small. The fuzzy S4 prepared as an initial configuration decays rapidly into this vacuum in the process of thermalization. Thus we find that the model does not possess a ``fuzzy S4 phase'' in contrast to our previous results on the fuzzy S2.
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