High Energy Physics - Theory
[Submitted on 4 Jun 2015 (v1), last revised 15 Jun 2015 (this version, v2)]
Title:Spinning the Fuzzy Sphere
View PDFAbstract: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 $\mathcal{N} = 1^*$ 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.
Submission history
From: Eric Dzienkowski [view email][v1] Thu, 4 Jun 2015 20:04:33 UTC (2,071 KB)
[v2] Mon, 15 Jun 2015 18:57:15 UTC (2,072 KB)
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