Black branes in asymptotically Lifshitz spacetime and viscosity/entropy ratios in Horndeski gravity

We investigate black brane solutions in asymptotically Lifshitz spacetime in 3+1-dimensional Horndeski gravity, which admit a critical exponent fixed at $z=1\mathrm{/}2$. The cosmological constant depends on $z$ as $\mathrm{\Lambda }=-(1+2z)\mathrm{/}{L}^2$. We compute the shear viscosity in the 2+1-dimensional dual boundary field theory via holographic correspondence. We investigate the violation of the bound for viscosity to entropy density ratio of $\eta \mathrm{/}s\ge 1\mathrm{/}(4\pi )$ at $z=1\mathrm{/}2$.