Chaos, diffusivity, and spreading of entanglement in magnetic branes, and the strengthening of the internal interaction

Abstract

Abstract We use holographic methods to study several chaotic properties of a super Yang-Mills theory at temperature T in the presence of a background magnetic field of constant strength B. The field theory we work on has a renormalization flow between a fixed point in the ultraviolet and another in the infrared, occurring in such a way that the energy at which the crossover takes place is a monotonically increasing function of the dimensionless ratio ℬ/T 2. By considering shock waves in the bulk of the dual gravitational theory, and varying ℬ/T 2, we study how several chaos-related properties of the system behave while the theory they live in follows the renormalization flow. In particular, we show that the entanglement and butterfly velocities generically increase in the infrared theory, violating the previously suggested upper bounds but never surpassing the speed of light. We also investigate the recent proposal relating the butterfly velocity with diffusion coefficients. We find that electric diffusion constants respect the lower bound proposed by Blake. All our results seem to consistently indicate that the global effect of the magnetic field is to strengthen the internal interaction of the system.