Chaos in the Mass-Deformed ABJM Model

TL;DR

This paper investigates chaotic behavior in the mass-deformed ABJM model by analyzing Lyapunov exponents and their relation to temperature, providing bounds for chaos compliance with the MSS bound.

Contribution

It introduces a reduced effective Lagrangian approach using fuzzy sphere configurations to study chaos in the mass-deformed ABJM model.

Findings

Largest Lyapunov exponent depends on energy and temperature.

Upper temperature bounds are identified for MSS chaos bound compliance.

Chaos behavior varies with matrix size and energy levels.

Abstract

Chaotic dynamics of the mass deformed ABJM model is explored. To do so, we consider spatially uniform fields and obtain a family of reduced effective Lagrangians by tracing over ansatz configurations involving fuzzy two-spheres with collective time dependence. We examine how the largest Lyapunov exponent, $\lambda_L$, changes as a function of $E/N^2$, where $N$ is the matrix size. In particular, we inspect the temperature dependence of $\lambda_L$ and present upper bounds on the temperature above which $\lambda_L$ values comply with the MSS bound, $ \lambda_L \leq 2 \pi T $, and below which it will eventually be not obeyed.