Spinning the Fuzzy Sphere

Abstract

We construct various exact analytical solutions of the $SO(3)$ BMN matrix model that correspond to rotating fuzzy spheres and rotating fuzzy tori.These are also solutions of Yang Mills theory compactified on a sphere times time and they are also translationally invariant solutions of the $\mathcal{N}=1^{\ast }$ field theory with a non-trivial charge density. The solutions we construct have a ${\mathbb{Z}}_N$ symmetry, where $N$ is the rank of the matrices. After an appropriate ansatz, we reduce the problem to solving a set of polynomial equations in $2N$ real variables. These equations have a discrete set of solutions for each value of the angular momentum. We study the phase structure of the solutions for various values of $N$. Also the continuum limit where $N\to \infty$, where the problem reduces to finding periodic solutions of a set of coupled differential equations. We also study the topology change transition from the sphere to the torus.

v2: Added references. Added comments

References in corpus (6)

• Building an AdS/CFT superconductor
• Three-dimensional N=6 SCFT's and their membrane dynamics
• Spinning squashed extra dimensions and chiral gauge theory from $\mathcal{N}=4$ SYM
• Dynamical tachyons on fuzzy spheres
• More Membrane Matrix Model Solutions - and Minimal Surfaces in S^7
• Classical Solutions in the BMN Matrix Model