The authors derive leading-order radial and angular stability spectra for two spherical BMN membrane configurations and demonstrate that next-to-leading-order couplings transfer dipole and quadrupole instabilities to all higher multipoles.
Noncommutative Algebraic Equations and Noncommutative Eigenvalue Problem
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abstract
We analyze the perturbation series for noncommutative eigenvalue problem $AX=X\lambda$ where $\lambda$ is an element of a noncommutative ring, $ A$ is a matrix and $X$ is a column vector with entries from this ring. As a corollary we obtain a theorem about the structure of perturbation series for Tr $x^r$ where $x$ is a solution of noncommutative algebraic equation (for $r=1$ this theorem was proved by Aschieri, Brace, Morariu, and Zumino, hep-th/0003228, and used to study Born-Infeld lagrangian for the gauge group $U(1)^k$).
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Turbulent aspects of BMN membrane dynamics
The authors derive leading-order radial and angular stability spectra for two spherical BMN membrane configurations and demonstrate that next-to-leading-order couplings transfer dipole and quadrupole instabilities to all higher multipoles.