Photoproduction and conductivity in dense holographic QCD

We explore the photoemission rate and conductivity in dense QCD by taking the AdS/CFT methods. Specifically, we take three QCD gravity dual models to do comparative studies: D4/D6 model, noncritical Sakai-Sugimoto model and soft-wall AdS/QCD model. We turn on the time component of flavor U(1) gauge field in the bulk side to model the baryon density in QCD. For all three models, we numerically solve the U(1) fluctuation equation to plot the spectral function and photoemission rate for lightlike momenta as well as the AC conductivity. We find that the results for the former two models are very similar to previous studies while the last one show some differences. The conductivity in the soft-wall model seems to be similar to that of holographic superconductor constructed from five-dimensional bulk gravity, i.e. the pseudogap structure. This should be owing to that the infrared (IR) soft-wall (an effective cutoff near the IR of the geometry) produces a mass gap in the dual field theory, which has imprinting in the conductivity as a pseudogap formation. However, the DC conductivity in our computations is finite while it should be a delta peak in holographic superconductor models. Our results show the importance of dilaton running in affecting physical quantities.

Figure 1

D4/D6 model: trace of the spectral function for lightlike momenta divided by frequency, ${\eta }^{\mu \nu }{\chi }_{\mu \nu }(q=\omega )/\omega$, in units of $\mathcal{N}$; different curves correspond to different dimensionless baryon density: $\tilde{d}=0$ (red), 2.0 (green), 4.0 (blue), 6.0 (black).

Figure 2

D4/D6 model: photoproduction rate $d\Gamma /d\omega$, weighted in units of $\mathcal{N}\frac{e^2}{4\pi }$, at different baryon density corresponding to Fig. 1.

Figure 3

D4/D6 model: real part of the AC conductivity corresponding to different baryon density $\tilde{d}=0.0$ (red), 1.0 (green), 2.0 (blue), 3.0 (black), 4.0 (yellow).

Figure 4

Noncritical Sakai-Sugimoto model: trace of the spectral function for lightlike momenta divided by frequency, ${\chi }_{\mu }^{\mu }(q=\omega )/\omega$; different curves correspond to different dimensionless baryon density: $\tilde{d}=0$ (red), 2.0 (green), 4.0 (blue), 6.0 (black).

Figure 5

Noncritical Sakai-Sugimoto model: photoproduction rate $d\Gamma /d\omega$ at different dimensionless baryon density corresponding to plots in Fig. 4.

Figure 6

Noncritical Sakai-Sugimoto model: real part of the AC conductivity corresponding to different baryon density: $\tilde{d}=0.0$ (red), 1.0 (green), 2.0 (blue), 3.0 (black), 4.0 (orange).

Figure 7

Super-Yang-Mills plasma: real part of the AC conductivity corresponding to different baryon density: $\tilde{d}=0.0$ (red), 1.0 (green), 2.0 (blue), 3.0 (black), 4.0 (orange).

Figure 8

Super-Yang-Mills plasma: trace of the spectral function for lightlike momenta divided by frequency, ${\chi }_{\mu }^{\mu }(q=\omega )/\omega$; different curves correspond to different dimensionless baryon density: $\tilde{d}=0$ (red), 2.0 (green), 4.0 (blue), 6.0 (black).

Figure 9

Super-Yang-Mills plasma: photoproduction rate $d\Gamma /d\omega$ at different dimensionless baryon density $\tilde{d}=0.0$ (red), 2.0 (green), 4.0 (blue), 6.0 (black).

Figure 10

Soft-wall model ($c=3$): trace of the spectral function for lightlike momenta divided by frequency, ${\chi }_{\mu }^{\mu }(q=\omega )/\omega$; different curves correspond to different dimensionless baryon density: $\tilde{d}=0.0$ (red), 2.0 (green), 4.0 (blue), 6.0 (black).

Figure 11

Soft-wall model ($c=3$): photoproduction rate $d\Gamma /d\omega$ at different dimensionless baryon density corresponding to plots in Fig. 10.

Figure 12

Soft-wall model ($c=3$): real part of the AC conductivity corresponding to different baryon density: $\tilde{d}=0.0$ (red), 1.0 (green), 2.0 (blue), 3.0 (black), 4.0 (orange).

Figure 13

Soft-wall model ($c=3$): trace of the spectral function for lightlike momenta divided by frequency, ${\chi }_{\mu }^{\mu }(q=\omega )/\omega$; different curves correspond to different dimensionless baryon density: $\tilde{d}=0.0$ (red), 0.1 (green), 0.2 (blue), 0.4 (black), 0.6 (orange).

Figure 14

Soft-wall model ($c=3$): photoproduction rate $d\Gamma /d\omega$ at different dimensionless baryon density corresponding to plots in Fig. 13.

Figure 15

Soft-wall model ($c=3$): real part of the AC conductivity corresponding to different baryon density: $\tilde{d}=0.1$ (red), 0.2 (green), 0.4 (blue), 0.6 (black), 0.8 (orange).