Note on Noether charge and holographic transports

TL;DR

This paper revisits Wald formalism to clarify the relation between Noether charge and equations of motion, proposing a new method to compute holographic transport coefficients like shear viscosity using horizon data.

Contribution

It introduces a novel approach linking Noether charge to holographic transport properties, enabling simple calculations of shear viscosity to entropy density ratio from black hole horizon data.

Findings

The method correctly reproduces shear viscosity to entropy density ratio for Einstein gravity.

It extends to Gauss-Bonnet gravity with matter fields, maintaining accuracy.

The approach provides a unified framework for holographic transport calculations.

Abstract

We clarify the relation between the Noether charge associated to an arbitrary vector field and the equations of motions by revisiting Wald formalism. For a time-like Killing vector, aspects of the Noether charge suggest that it is dual to the heat current in the boundary for general holographic theories. For a space-like Killing vector, we interpret the Noether charge (at the transverse direction) as shear stress of the dual fluid so we can compute the ratio of shear viscosity to entropy density by simply using the infrared data on the black hole event horizon. We test the new method for Einstein gravity and Gauss-Bonnet gravity and find that it produces correct results for both cases even in the presence of additional matter fields.