The Stability of Noncommutative Scalar Solitons

Abstract

We determine the stability conditions for a radially symmetric noncommutative scalar soliton at finite noncommutivity parameter $\theta$. We find an intriguing relationship between the stability and existence conditions for all level-1 solutions, in that they all have nearly-vanishing stability eigenvalues at critical $\theta m^2$. The stability or non-stability of the system may then be determined entirely by the ${\varphi }^3$ coefficient in the potential. For higher-level solutions we find an ambiguity in extrapolating solutions to finite $\theta$ which prevents us from making any general statements. For these stability may be determined by comparing the fluctuation eigenvalues to critical values which we calculate.

12 pages, corrected typos

Cited by in corpus (8)

• Analytic Study of Nonperturbative Solutions in Open String Field Theory
• Discrete Nonlocal Waves
• Noncommutative solitons on Kahler manifolds
• Scalar Multi-Solitons on the Fuzzy Sphere
• Scalar Solitons on the Fuzzy Sphere
• A note on noncommutative scalar multisolitons
• Lattice vortices induced by noncommutativity
• On the Moduli Space of Noncommutative Multi-solitons at Finite Theta