We study the holographic dual of a massive gravity with Gauss-Bonnet and
cubic quasi-topological higher curvature terms. Firstly, we find the
energy-momentum two-point function of the 4-dimensional boundary theory where
the massive term breaks the conformal symmetry as expected. An a-theorem is
introduced based on the null energy condition. Then we focus on a black brane
solution in this background and derive the ratio of shear viscosity to entropy
density for the dual theory. It is worth mentioning that the concept of
viscosity as a transport coefficient is obscure in a nontranslational invariant
theory as in our case. So although we use the Green-Kubo's formula to derive
it, we rather call it the rate of entropy production per the Planckian time due
to a strain. Results smoothly cover the massless limit.Comment: v2: 20 pages, typo corrected, references added; v3: section 2.2
revised; v4: section 2.2 modified, viscosity formula revised, 2 figs added,
references added; v5: 23 pages, a sign mistake in eq. (74) fixed (results
modified), eq. (34) modified, one fig added, refs added, to appear in EPJ
