Rotating black branes in $f(R)$ gravity coupled to nonlinear Maxwell field

A class of higher dimensional rotating solutions in $R+f(R)$ theory coupled to a conformally invariant Maxwell field is presented. These solutions have asymptotically anti–de Sitter behavior but exist only for dimensions which are multiples of four. These solutions represent black branes with cylindrical or toroidal horizons and $k$ rotation parameters. We present the suitable counterterm which removes the divergences of the action in $R+f(R)$ gravity with constant curvature. We also compute the mass, the angular momenta, the entropy, the charge, and the electric potential of the black branes. Finally, we check that the conserved and thermodynamic quantities satisfy the first law of thermodynamics.