It was shown by Buchbinder, Buchel, and Vazquez [J. High Energy Phys. 12 (2008) 090] that, in the presence of the magnetic field, the sound waves in ($2+1$)-dimensional plasma disappear and are replaced by a diffusive mode. Similarly, the shear and charge diffusion fluctuations form a subdiffusive mode. However, since the limit of a 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 the $M2$-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 a 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 an external magnetic field.

• Received 12 December 2008

DOI:https://doi.org/10.1103/PhysRevD.79.046006