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We perform nonperturbative studies of the dimensionally reduced 5dYang-Mills-Chern-Simons model, in which a four-dimensional fuzzy manifold,``fuzzy S$^{4}$'', is known to exist as a classical solution. Although theaction is unbounded from below, Monte Carlo simulations provide an evidence fora well-defined vacuum, which stabilizes at large $N$, when the coefficient ofthe Chern-Simons term is sufficiently small. The fuzzy S$^{4}$ prepared as aninitial configuration decays rapidly into this vacuum in the process ofthermalization. Thus we find that the model does not possess a ``fuzzy S$^{4}$phase'' in contrast to our previous results on the fuzzy S$^{2}$.Comment: 11 pages, 2 figures, (v2) typos correcte

Absence of a fuzzyS4phase in the dimensionally reduced 5d Yang-Mills-Chern-Simons model

Absence of a fuzzyS⁴phase in the dimensionally reduced 5d Yang-Mills-Chern-Simons model