Fluid/gravity correspondence: A nonconformal realization in compactified D4 branes

TL;DR

This paper extends the fluid/gravity correspondence framework to nonconformal backgrounds using compactified D4-branes, deriving transport coefficients for nonconformal gluonic matter and validating the approach through viscosity and sound speed ratios.

Contribution

It develops a boundary derivative expansion formalism for nonconformal D4-brane backgrounds and computes first-order transport coefficients, confirming their consistency with established methods.

Findings

Derived 5D Einstein gravity with scalar fields from 10D D4-branes.

Calculated first-order transport coefficients for nonconformal gluonic matter.

Validated results through agreement with Green-Kubo method.

Abstract

We develop the framework of boundary derivative expansion (BDE) formalism of fluid/gravity correspondence in compactified D4-brane system, which is a nonconformal background used in top-down holographic QCD models. Such models contain the D4-D6 model and the Sakai-Sugimoto (SS) model, with the background of the compactified black D4 branes under the near horizon limit. By using the dimensional reduction technique, we derive a 5D Einstein gravity minimally coupled with 3 scalar fields from the 10D D4-brane background. Following the BDE formalism of fluid/gravity correspondence in the conformal background, we directly derive all the first order transport coefficients for nonconformal gluonic matter. The results of the ratio of the bulk to shear viscosity and the sound speed agree with those obtained from the Green-Kubo method. This agreement guarantees the validity of the BDE formalism of fluid/gravity duality in the nonconformal D-brane background, which can be used to calculate the second order transport coefficients in nonconformal background.