Dynamical tachyons on fuzzy spheres

Abstract

We study the spectrum of off-diagonal fluctuations between displaced fuzzy spheres in the BMN plane wave matrix model. The displacement is along the plane of the fuzzy spheres. We find that when two fuzzy spheres intersect at angles classical tachyons develop and that the spectrum of these modes can be computed analytically. These tachyons can be related to the familiar Nielsen-Olesen instabilities in Yang-Mills theory on a constant magnetic background. Many features of the problem become more apparent when we compare with maximally supersymmetric Yang-Mills on a sphere, of which this system is a truncation. We also set up a simple oscillatory trajectory on the displacement between the fuzzy spheres and study the dynamics of the modes as they become tachyonic for part of the oscillations. We speculate on their role regarding the possible thermalization of the system.

34 pages, 4 figures; v2: 35 pages, expanded sec. 4.3, added references

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Cited by in corpus (9)

• Evidence for fast thermalization in the plane-wave matrix model
• Matrix embeddings on flat $R^3$ and the geometry of membranes
• The smallest matrix black hole model in the classical limit
• Black Hole Formation in Fuzzy Sphere Collapse
• Black Hole Formation at the Correspondence Point
• Quantum Black Hole Formation in the BFSS Matrix Model
• From Black Hole to Qubits: Evidence of Fast Scrambling in BMN theory
• Thermalization in massive deformations of Yang-Mills matrix models
• Spinning the Fuzzy Sphere