Abstract
We study classical chaotic motions in the Berenstein-Maldacena-Nastase (BMN) matrix model. For this purpose, it is convenient to focus upon a reduced system composed of two-coupled anharmonic oscillators by supposing an ansatz. We examine three ansätze: 1) two pulsating fuzzy spheres, 2) a single Coulomb-type potential, and 3) integrable fuzzy spheres. For the first two cases, we show the existence of chaos by computing Poincaré sections and a Lyapunov spectrum. The third case leads to an integrable system. As a result, the BMN matrix model is not integrable in the sense of Liouville, though there may be some integrable subsectors.
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Asano, Y., Kawai, D. & Yoshida, K. Chaos in the BMN matrix model. J. High Energ. Phys. 2015, 191 (2015). https://doi.org/10.1007/JHEP06(2015)191
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DOI: https://doi.org/10.1007/JHEP06(2015)191