Absence of a fuzzy $S^4$ phase in the dimensionally reduced 5d Yang-Mills-Chern-Simons model

TL;DR

This study investigates the 5d Yang-Mills-Chern-Simons model and finds that, unlike the fuzzy S$^{2}$ case, the fuzzy S$^{4}$ phase does not exist as a stable vacuum in the nonperturbative regime.

Contribution

The paper provides the first nonperturbative evidence that the fuzzy S$^{4}$ phase is absent in the dimensionally reduced 5d Yang-Mills-Chern-Simons model.

Findings

Fuzzy S$^{4}$ decays into the stable vacuum rapidly.

The model stabilizes at large N with small Chern-Simons coefficient.

No fuzzy S$^{4}$ phase observed in simulations.

Abstract

We perform nonperturbative studies of the dimensionally reduced 5d Yang-Mills-Chern-Simons model, in which a four-dimensional fuzzy manifold, ``fuzzy S$^{4}$'', 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 S$^{4}$ 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 S$^{4}$ phase'' in contrast to our previous results on the fuzzy S$^{2}$.