Perturbative versus nonperturbative dynamics of the fuzzy S^2*S^2

TL;DR

This paper investigates the dynamics of fuzzy S^2*S^2 and S^2 solutions in a matrix model with a cubic term, analyzing their decay, stability, and the universality of large-N behavior through perturbative calculations and Monte Carlo simulations.

Contribution

It provides a detailed comparison of perturbative and nonperturbative dynamics of fuzzy spheres in a matrix model, revealing universality in large-N behavior of fuzzy manifolds.

Findings

Both solutions decay into the Yang-Mills vacuum below a critical cubic coefficient.

Perturbation theory accurately reproduces results above the critical point.

Decay probability of fuzzy S^2*S^2 into fuzzy S^2 is suppressed at large N.

Abstract

We study a matrix model with a cubic term, which incorporates both the fuzzy S^2*S^2 and the fuzzy S^2 as classical solutions. Both of the solutions decay into the vacuum of the pure Yang-Mills model (even in the large-N limit) when the coefficient of the cubic term is smaller than a critical value, but the large-N behavior of the critical point is different for the two solutions. The results above the critical point are nicely reproduced by the all order calculations in perturbation theory. By comparing the free energy, we find that the true vacuum is given either by the fuzzy S^2 or by the ``pure Yang-Mills vacuum'' depending on the coupling constant. In Monte Carlo simulation we do observe a decay of the fuzzy S^2*S^2 into the fuzzy S^2 at moderate N, but the decay probability seems to be suppressed at large N. The above results, together with our previous results for the fuzzy CP^2, reveal certain universality in the large-N dynamics of four-dimensional fuzzy manifolds realized in a matrix model with a cubic term.