Sound waves in the compactified D0-D4 brane system

TL;DR

This paper investigates how the presence of smeared D0-branes affects sound wave propagation in a holographic QCD model, revealing modifications to sound speed and attenuation related to the Chern-Simons coupling.

Contribution

It derives the effective 5d theory for the D0-D4 system and analytically computes sound mode properties, highlighting the influence of D0-branes on transport phenomena.

Findings

Sound speed is altered by D0-branes.

Sound wave attenuation depends on D0-brane density.

Results connect D0-brane effects to the Chern-Simons coupling in dual QCD.

Abstract

As an extension to our previous work, we study the transport properties of the Witten-Sakai-Sugimoto model in the black D4-brane background with smeared D0-branes (D0-D4/D8 system). Because of the presence of the D0-branes, in the bubble configuration this model is holographically dual to 4d QCD or Yang-Mills theory with a Chern-Simons term. And the number density of the D0-branes corresponds to the coupling constant ($\theta$ angle) of the Chern-Simons term in the dual field theory. In this paper, we accordingly focus on small number density of the D0-branes to study the sound mode in the black D0-D4 brane system since the coupling of the Chern-Simons term should be quite weak in QCD. Then we derive its 5d effective theory and analytically compute the speed of sound and the sound wave attenuation in the approach of Gauge/Gravity duality. Our result shows the speed of sound and the sound wave attenuation is modified by the presence of the D0-branes. Thus they depend on the $\theta$ angle or chiral potential in this holographic description.