Shear viscosity from black holes in generalized scalar-tensor theories in arbitrary dimensions

In higher dimensions, we study Degenerate-Higher-Order-Scalar-Tensor theories and we derive solutions that resemble the Schwarzschild Anti-de Sitter black holes. We compute their thermodynamic quantities following the Wald formalism, satisfying the First Law of Thermodynamics and a higher dimensional Smarr relation. Constructing a Noether charge with a suitable choice of a space-like Killing vector, we obtain the shear viscosity of the non-gravitational dual field theory, where for a suitable choice of the couplings functions, the Kovtun-Son-Starinets bound is violated. These results are corroborated by the calculation of the Green’s functions following the Kubo formalism.