Axionic black branes in the k-essence sector of the Horndeski model

We construct new black brane solutions in the context of Horndeski gravity, in particular, in its K-essence sector. These models are supported by axion scalar fields that depend only on the horizon coordinates. The dynamics of these fields is determined by a K-essence term that includes the standard kinetic term X and a correction of the form X-k. We find both neutral and charged exact and analytic solutions in D-dimensions, which are asymptotically anti-de Sitter. Then, we describe in detail the thermodynamical properties of the four-dimensional solutions and we compute the dual holographic DC conductivity.