The Fate of the Sound and Diffusion in Holographic Magnetic Field

TL;DR

This paper investigates the behavior of sound, shear, and charge diffusion modes in (2+1)D plasma under magnetic fields using AdS/CFT, confirming their stability and universality of shear viscosity in strong magnetic fields.

Contribution

It demonstrates the existence and stability of diffusion modes in M2-brane plasma under magnetic fields and computes related transport coefficients to all orders.

Findings

Diffusion modes persist in M2-brane plasma with magnetic fields.

Shear viscosity to entropy ratio saturates the KSS bound.

Transport coefficients are computed to all orders in magnetic field.

Abstract

It was shown in arXiv:0810.4094 [hep-th] that in the presence of the magnetic field the sound waves in (2+1) dimensional plasma disappear and are replaces by a diffusive mode. Similarly, the shear and charge diffusion fluctuations form a subdiffusive mode. However, since the limit of small magnetic field does not commute with the hydrodynamic limit it is not obvious whether or not these modes are stable under higher order corrections. Using AdS/CFT correspondence we show that in the case of M2-brane plasma these modes do exist as we find the corresponding supergravity solutions. This allowed us to compute the conductivity and the shear viscosity to all orders in magnetic field. We find that the viscosity to entropy ratio saturates the Kovtun-Son-Starinets bound. This extends the universality property of the shear viscosity to the case of the strongly coupled plasma in external magnetic field.