Absence of a fuzzy S phase in the dimensionally reduced 5d Yang-Mills-Chern-Simons model

We perform nonperturbative studies of the dimensionally reduced 5d YangMills-Chern-Simons model, in which a four-dimensional fuzzy manifold, “fuzzy S”, is known to exist as a classical solution. Although the action is unbounded from below, a well-defined vacuum, which stabilizes at large N , exists when the coefficient of the ChernSimons term is sufficiently small. However, this vacuum corresponds to the “Yang-Mills phase”, in which the system behaves similarly to the pure Yang-Mills model. In Monte Carlo simulations we find that the fuzzy S prepared as an initial configuration either diverges or falls into the Yang-Mills phase. Thus the model does not have a “fuzzy S phase” in contrast to our previous results on the dimensionally reduced 3d Yang-MillsChern-Simons model, in which the “fuzzy S” can be realized dynamically.