Mesonic quasinormal modes of the Sakai-Sugimoto model at high temperature

We examine the mesonic thermal spectrum of the Sakai-Sugimoto model of holographic QCD by finding the quasinormal frequencies of the supergravity dual. If flavor is added using D8-$\overline{\mathrm{D}8}$ branes there exist embeddings where the D-brane world volume contains a black hole. For these embeddings (the high-temperature phase of the Sakai-Sugimoto model) we determine the quasinormal spectra of scalar and vector mesons arising from the world volume Dirac-Born-Infeld (DBI) action of the D-brane. We stress the importance of a coordinate change that makes the infalling quasinormal modes regular at the horizon allowing a simple numerical shooting technique. Finally we examine the effect of finite spatial momentum on quasinormal spectra.

Figure 1

The lowest five $k=0$ Klein-Gordon scalar quasinormal frequencies in the complex $\omega$ plane.

Figure 2

The lowest five $k=0$ sigma meson quasinormal frequencies in the complex $\omega$ plane.

Figure 3

The lowest five static vector meson quasinormal frequencies in the complex $\omega$ plane.

Figure 4

Lowest quasinormal frequencies at finite real spatial momentum $k$ in the complex $\omega$ plane for the scalar $\overline{q}q$ bound state. The momentum $k$ ranges from 0 to 5.0 in steps of 0.5 (in the same units as $\omega$) as one moves to the right in the plot.

Figure 5

On the left we show the lowest vector $\overline{q}q$ bound state quasinormal frequencies at finite real spatial momentum $k$ in the complex $\omega$ plane. The momentum ranges from 0 to 2.0 in steps of 0.2 as one moves to the right (the lowest mode in the longitudinal spectrum, corresponding to the diffusion pole in the hydrodynamic limit, is excluded). For each mode the flatter trajectory corresponds to the transverse species and the steeper to the longitudinal. On the right we show the momentum dependence of the lowest quasinormal mode for the longitudinal vector meson. The equation of the line is $y=\log \frac{2}{3}+2x$ showing the validity of the relation $\omega =-iD{k}^2$ for small $k$, with $D=\frac{2}{3}$.