Fluid/gravity correspondence: Second order transport coefficients in compactified D4-branes

TL;DR

This paper extends the fluid/gravity correspondence to nonconformal fluids by calculating nine second order transport coefficients for a holographic model based on compactified D4-branes, ensuring causality and relation consistency.

Contribution

It develops a boundary derivative expansion formalism for nonconformal fluids and explicitly computes second order transport coefficients for the D4-brane holographic dual.

Findings

Calculated nine second order transport coefficients.

Confirmed the fluid's causality and the Haack-Yarom relation.

Provided explicit formulas for nonconformal relativistic fluids.

Abstract

We develop the boundary derivative expansion (BDE) formalism of fluid/gravity correspondence to nonconformal version through the compactified, near-extremal black D4-brane. We offer an explicit calculation of 9 second order transport coefficients, i.e., the $\tau_\pi,~\tau_\pi^*,~\tau_\Pi,~\lambda_{1,2,3}$ and $\xi_{1,2,3}$ for the strongly coupled, uncharged and nonconformal relativistic fluid which is the holographic dual of compactified, near extremal black D4-brane. We also show that the nonconformal fluid considered in this work is free of causal problem and admits the Haack-Yarom relation $4\lambda_1+\lambda_2=2\eta\tau_\pi$.