Stability of the fuzzy sphere solution from matrix model

TL;DR

This paper investigates the stability of the fuzzy sphere solution in a matrix model, identifying conditions under which it remains stable or becomes unstable based on a parameter .

Contribution

It provides a detailed analysis of the classical stability of the fuzzy sphere in a matrix model, revealing the parameter range for stability and instability.

Findings

Fuzzy sphere is stable for  

Unstable for  < 1/2

New classical solutions found for  < 1

Abstract

We consider a matrix model depending on a parameter $\lambda$ which permits the fuzzy sphere as a classical background.By expanding the bosonic matrices around this background ones recovers a U(1) (U(n)) noncommutative gauge theory on the fuzzy sphere. To check classical stability of this background, we look for new classical solutions of this model and find them for $\lambda < 1$, that make the fuzzy sphere solution unstable for $\lambda < \half$ and stable otherwise. \\