The Viscosity Bound Conjecture and Hydrodynamics of M2-Brane Theory at Finite Chemical Potential
Omid Saremi
TL;DR
The paper tests the Kovtun–Son–Starinets viscosity bound in the M2-brane theory at finite chemical potential by studying axial perturbations of R-charged AdS4 black holes via the Minkowski AdS/CFT prescription. It develops a horizon-centered, series-based solution to a coupled system of gravitational and gauge-field perturbations and extracts the diffusion pole to compute η/s. The key finding is that η/s remains saturated at 1/(4π) up to fourth order in the dimensionless ratio Ω/T_H, even as μ (and Ω) are turned on, while η itself increases with μ. This supports a universal saturation of the bound tied to black hole horizon physics, with potential implications for holographic hydrodynamics and entropy bounds in strongly coupled plasmas.
Abstract
Kovtun, Son and Starinets have conjectured that the viscosity to entropy density ratio $η/s$ is always bounded from below by a universal multiple of $\hbar$ i.e., $\hbar/(4πk_{B})$ for all forms of matter. Mysteriously, the proposed viscosity bound appears to be saturated in all computations done whenever a supergravity dual is available. We consider the near horizon limit of a stack of M2-branes in the grand canonical ensemble at finite R-charge densities, corresponding to non-zero angular momentum in the bulk. The corresponding four-dimensional R-charged black hole in Anti-de Sitter space provides a holographic dual in which various transport coefficients can be calculated. We find that the shear viscosity increases as soon as a background R-charge density is turned on. We numerically compute the few first corrections to the shear viscosity to entropy density ratio $η/s$ and surprisingly discover that up to fourth order all corrections originating from a non-zero chemical potential vanish, leaving the bound saturated. This is a sharp signal in favor of the saturation of the viscosity bound for event horizons even in the presence of some finite background field strength. We discuss implications of this observation for the conjectured bound.