Axionic charged black branes with arbitrary scalar nonminimal coupling

Abstract

Abstract In this paper, we construct four-dimensional charged black branes of a nonminimally coupled and self-interacting scalar field. In addition to the scalar and Maxwell fields, the model involves two axionic fields homogeneously distributed along the two-dimensional planar base manifold providing in turn a simple mechanism of momentum dissipation. Interestingly enough, the horizon of the solution can be located at two different positions depending on the sign of the parameter associated to the axionic field, and in both cases there exists a wide range of values of the nonminimal coupling parameter yielding to physical acceptable solutions. For a negative parameter that sustains the axionic fields, the allowed nonminimal coupling parameters take discrete values and the solution turns out to be extremal since its has zero temperature. A complete analysis of the thermodynamic features of the solutions is also carried out. Finally, thanks to the mechanism of momentum dissipation, the holographic DC conductivities of the solutions are computed in terms of the black hole horizon data, and we analyze the effects of the nonminimal coupling parameter on these conductivities. For example, in the purely electric case, we notice that as long as the nonminimal coupling parameter takes the discrete values associated to the extremal solution, the DC conductivity vanishes identically reproducing in turn an insulator behavior. In the non extremal case, we point out the existence of a particular value of the nonminimal coupling parameter (which is greater than the conformal one in four dimensions) yielding an infinite conductivity; this is due to the fact that the translation invariance is restored at this point. Finally, in the dyonic case, we show that the conductivity matrix for the extremal solution has a Hall effect-like behavior.