# Linear-$T$ resistivity from low to high temperature: axion-dilaton theories

## TL;DR

This paper extends the holographic analysis of linear-$T$ resistivity from low to high temperatures in axion-dilaton theories, identifying key conditions like strong momentum relaxation and specific couplings necessary for this behavior.

## Contribution

It demonstrates that strong momentum relaxation alone is not sufficient for high-temperature linear-$T$ resistivity, highlighting the role of the dilaton-Maxwell coupling in this phenomenon.

## Key findings

- Strong momentum relaxation is necessary for high-temperature linear-$T$ resistivity.
- Only limited parameter ranges support linear-$T$ resistivity up to high temperature.
- Incoherent conductivity and dilaton-Maxwell coupling are crucial for robust linear-$T$ resistivity.

## Abstract

The linear-$T$ resistivity is one of the hallmarks of various strange metals regardless of their microscopic details. Towards understanding this universal property, the holographic method or gauge/gravity duality has made much progress. Most holographic models have focused on the low temperature limit, where the linear-$T$ resistivity has been explained by the infrared geometry. We extend this analysis to high temperature and identify the conditions for a robust linear-$T$ resistivity up to high temperature. This extension is important because, in experiment, the linear-$T$ resistivity is observed in a large range of temperatures, up to room temperature. In the axion-dilaton theories we find that, to have a robust linear-$T$ resistivity, the strong momentum relaxation is a necessary condition, which agrees with the previous result for the Guber-Rocha model. However, it is not sufficient in the sense that, among large range of parameters giving a linear-$T$ resistivity in low temperature limit, only very limited parameters can support the linear-$T$ resistivity up to high temperature even in strong momentum relaxation. We also show that the incoherent term in the general holographic conductivity formula or the coupling between the dilaton and Maxwell term is responsible for a robust linear-$T$ resistivity up to high temperature.