PHYSICAL REVIEW D, vol.107, no.6, 2023 (SCI-Expanded)
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-GomezVan 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 alpha (E/N-2)(1/3) or lambda L alpha (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.L values comply with the MaldacenaShenker-Stanford bound, lambda L <= 2 pi T, and below which it will eventually be not obeyed.