Sound waves in the compactified D0-D4 brane system

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 four-dimensional QCD or Yang-Mills theory with a Chern-Simons term, and the number density of the D0 branes corresponds to the coupling constant ($\ensuremath{\theta}$ angle) of the Chern-Simons term in the dual field theory. In this paper, we accordingly focus on the 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 five-dimensional 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 are modified by the presence of the D0 branes. Thus, they depend on the $\ensuremath{\theta}$ angle or chiral potential in this holographic description.