Date

2023-03-01

Author

Kürkcüoğlu, Seçkin
Başkan, Kagan
Taşcı, Cankat

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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, λ L , changes as a function of E / N 2 . Depending on the structure of the effective potentials, we find either λ L ∝ ( E / N 2 ) 1 / 3 or λ L ∝ ( E / N 2 − γ N ) 1 / 3 , where γ N ( k , μ ) are constants determined in terms of the Chern-Simons coupling k , the mass μ , 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 λ L values comply with the Maldacena-Shenker-Stanford bound, λ L ≤ 2 π T , and below which it will eventually be not obeyed.

URI

https://journals.aps.org/prd/pdf/10.1103/PhysRevD.107.066006
https://hdl.handle.net/11511/102693

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Department of Physics, Article