Transport Coefficients at Zero Temperature from Extremal Black Holes

TL;DR

This paper uses the AdS/CFT correspondence to analyze transport coefficients like shear viscosity and conductivity at zero temperature in strongly-coupled (2+1)-dimensional field theories, revealing universal low-frequency scaling behaviors linked to the near-horizon AdS_2 geometry.

Contribution

It demonstrates that shear viscosity to entropy density ratio remains 1/4π at zero temperature for extremal black holes and extends the analysis of low-frequency conductivity behavior to various dimensions and magnetic fields.

Findings

Shear viscosity to entropy density ratio is 1/4π at zero temperature.

Low-frequency conductivity exhibits universal scaling due to AdS_2 near-horizon geometry.

Conductivity behavior persists across different dimensions and magnetic field conditions.

Abstract

Using the AdS/CFT correspondence we study transport coefficients of a strongly-coupled (2 +1)-dimensional field theory at {\it zero} temperature and finite charge density. The field theory under consideration is dual to the extremal Reissner-Nordstrom AdS_4 black hole in the bulk. We show that, like the cases of scalar and spinor operators studied in \cite{Faulkner:2009wj}, the correlators of charge (vector) current and energy-momentum (tensor) operators exhibit scaling behavior at low frequency. The existence of such low frequency behavior is related to the fact that the near-horizon geometry of the extremal black hole background has an AdS_2 factor. We carefully calculate the shear viscosity (at zero temperature) and show that the ratio of the shear viscosity to the entropy density takes the value of 1/4\pi. Because of the AdS_2 factor, we argue that this result stays the same for all d-dimensional boundary field theories dual to the extremal Reissner-Nordstrom AdS_{d+1} black holes. Also, we compute the charge conductivity at zero temperature. The limiting behavior of the conductivity for small frequencies is also attributed to the near horizon AdS_2 factor and is argued to hold regardless of the dimension of the zero-temperature boundary field theory. Finally, using the extremal dyonic AdS_4 black hole as the background, we extract the conductivity in the presence of a constant magnetic field.