Holographic RG flow of the shear viscosity to entropy density ratio in strongly coupled anisotropic plasma

We study holographic RG flow of the shear viscosity tensor of anisotropic, strongly coupled N = 4 super-Yang-Mills plasma by using its type IIB supergravity dual in anisotropic bulk spacetime. We find that the shear viscosity tensor has three independent components in the anisotropic bulk spacetime away from the boundary, and one of the components has a non-trivial RG flow while the other two have a trivial one. For the component of the shear viscosity tensor with non-trivial RG flow, we derive its RG flow equation, and solve the equation analytically to second order in the anisotropy parameter 'a'. We derive the RG equation using the equation of motion, holographic Wilsonian RG method, and Kubo's formula. All methods give the same result. Solving the equation, we find that the ratio of the component of the shear viscosity tensor to entropy density eta/s flows from above 1/4 pi at the horizon (IR) to below 1/4 pi at the boundary (UV) where it violates the holographic shear viscosity (Kovtun-Son-Starinets) bound and where it agrees with the other longitudinal component.