Impact of supersymmetry on the nonperturbative dynamics of fuzzy spheres

TL;DR

This paper investigates how supersymmetry influences the stability and dynamics of fuzzy spheres in a 4d supersymmetric matrix model, revealing enhanced stability and specific eigenvalue behaviors compared to bosonic models.

Contribution

It demonstrates that supersymmetry stabilizes fuzzy spheres in the large-N limit and explores the eigenvalue distribution, contrasting with bosonic models where decay occurs.

Findings

Fuzzy spheres remain stable in supersymmetric models at large N.

Eigenvalue distributions lose power-law tails with fuzzy sphere presence.

Coincident fuzzy spheres are unstable, indicating a U(1) gauge group.

Abstract

We study a 4d supersymmetric matrix model with a cubic term, which incorporates fuzzy spheres as classical solutions, using Monte Carlo simulations and perturbative calculations. The fuzzy sphere in the supersymmetric model turns out to be always stable if the large-N limit is taken in such a way that various correlation functions scale. This is in striking contrast to analogous bosonic models, where the fuzzy sphere decays into the pure Yang-Mills vacuum due to quantum effects when the coefficient of the cubic term becomes smaller than a critical value. We also find that the power-law tail of the eigenvalue distribution, which exists in the supersymmetric model without the cubic term, disappears in the presence of the fuzzy sphere in the large-N limit. Coincident fuzzy spheres turn out to be unstable, which implies that the dynamically generated gauge group is U(1).