Violation of Thermal Conductivity Bound in Horndeski Theory

Abstract

We consider AdS black planar black hole in the four-dimensional Einstein-Maxwell-Horndeski theory with two free axions and analyse the thermodynamics of the black hole. We calculate the holographic thermoelectric conductivities of the dual field theory and determine the ratio of thermal conductivity over the temperature. At low temperature with zero electric current, we find that the ratio is proportional to temperature squared and hence can arbitrarily approach zero, providing an example that violates the thermal conductivity bound proposed in [arXiv:1511.05970].