Chaotic Dynamics of the Mass Deformed ABJM Model

Abstract

We explore the chaotic dynamics of the mass-deformed Aharony-Bergman-Jafferis-Maldacena model. To do so, we first perform a dimensional reduction of this model from $2+1$ to $0+1$ dimensions, considering that the fields are spatially uniform. Working in the 't Hooft limit and tracing over ansatz configurations involving fuzzy 2-spheres, which are described in terms of the Gomis-Rodriguez-Gomez-Van Raamsdonk-Verlinde matrices with collective time dependence, we obtain a family of reduced effective Lagrangians and demonstrate that they have chaotic dynamics by computing the associated Lyapunov exponents. In particular, we focus on how the largest Lyapunov exponent, ${\lambda }_L$, changes as a function of $E/N^2$. Depending on the structure of the effective potentials, we find either ${\lambda }_L\propto (E/N^2{)}^{1/3}$ or ${\lambda }_L\propto (E/N^2-{\gamma }_N{)}^{1/3}$, where ${\gamma }_N(k,\mu )$ are constants determined in terms of the Chern-Simons coupling $k$, the mass $\mu$, and the matrix level $N$. Noting that the classical dynamics approximates the quantum theory only in the high-temperature regime, we investigate the temperature dependence of the largest Lyapunov exponents and give upper bounds on the temperature above which ${\lambda }_L$ values comply with the Maldacena-Shenker-Stanford bound, ${\lambda }_L\le 2\pi T$, and below which it will eventually be not obeyed.

arXiv comment37 pages, 8 figures, published version

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Cited by in corpus (1)

• Chaos in the holographic matrix models for meson and baryon