Violation of Thermal Conductivity Bound in Horndeski Theory

TL;DR

This paper demonstrates that in a specific Horndeski gravity setup, the thermal conductivity to temperature ratio can approach zero at low temperatures, violating previously proposed universal bounds.

Contribution

It provides the first example within Horndeski theory where the thermal conductivity bound is violated, expanding understanding of transport properties in holographic models.

Findings

Thermal conductivity over temperature approaches zero at low T.

The model violates the proposed universal thermal conductivity bound.

Holographic thermoelectric conductivities are explicitly calculated.

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].