Stability of the fuzzy sphere solution from matrix model

Abstract

We consider a matrix model depending on a parameter $λ$ 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 $λ< 1$, that make the fuzzy sphere solution unstable for $λ< \half$ and stable otherwise. \\