The instability of intersecting fuzzy spheres

TL;DR

This paper investigates the classical and quantum stability of intersecting fuzzy spheres in reduced Yang-Mills-Chern-Simons models, revealing their instability and conditions for stability in specific configurations.

Contribution

It provides a one-loop perturbative analysis of fuzzy sphere configurations, highlighting their stability properties and the impact of supersymmetry and geometry.

Findings

Intersecting fuzzy spheres are classically unstable in studied models.

Concentric fuzzy spheres with different radii are perturbatively stable.

Stability depends on supersymmetry and sphere configuration.

Abstract

We discuss the classical and quantum stability of general configurations representing many fuzzy spheres in dimensionally reduced Yang-Mills-Chern-Simons models with and without supersymmetry. By performing one-loop perturbative calculations around such configurations, we find that intersecting fuzzy spheres are classically unstable in the class of models studied in this paper. We also discuss the large-N limit of the one-loop effective action as a function of the distance of fuzzy spheres. This shows, in particular, that concentric fuzzy spheres with different radii, which are identified with the 't Hooft-Polyakov monopoles, are perturbatively stable in the bosonic model and in the D=10 supersymmetric model.