Electromagnetic signature in holographic plasma with $B$ field

We explore the effect of a magnetic field on the electromagnetic signature in QCD-like plasma by taking the AdS/CFT approach. Concretely, we choose two QCD gravity dual models to do comparative studies: the D4/D6 and D3/D7 models. The magnetic field is simulated by a spatial component of the flavor U(1) gauge field in the bulk side. For both models, we plot the spectral function and photoemission rate for lightlike momenta as well as the ac conductivity. Due to the presence of the magnetic field, the rotational symmetry is partially broken. Therefore, we plot the spectral function and photoemission rate with spatial momentum parallel or perpendicular to the magnetic field, respectively. We find that the magnetic field induces an anisotropic feature in the electromagnetic signature. To be specific, when the emitted photons from the plasma are moving along the magnetic field, the electromagnetic signature is weakened as the magnetic field is increasing; on the contrary, when the produced photons move perpendicular to the magnetic field, the magnetic field has the effect of amplifying the electromagnetic signature. This should have a relationship with the anisotropic feature of the photon signal observed in heavy-ion collision experiments. This anisotropic characteristic can also be observed in the ac conductivity of the holographic plasma. In the infrared regime of the frequency, the magnetic field suppresses the ac conductivity (along the direction perpendicular to the magnetic field) and likely gives a pseudogap structure. However, the ac conductivity along the magnetic field is enhanced due to the presence of the magnetic field.

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 $\mathcal{N}$, for the case $\overrightarrow{k}\parallel B$. Different curves correspond to different dimensionless magnetic fields: $\tilde{B}$=0 (red, thick solid), 0.5 (green, solid), 1.0 (blue, dashed), 1.5 (black, dotted), 2.0 (orange, thick dashed), and 4.0 (pink, thick dotted).

Figure 2

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 $\mathcal{N}$, for the case $\overrightarrow{k}\perp B$. Different curves correspond to different dimensionless magnetic fields: $\tilde{B}$=0 (red, thick solid), 0.5 (green, solid), 1.0 (blue, dashed), 1.5 (black, dotted), and 2.0 (orange, thick dashed).

Figure 3

D4/D6 model: photoproduction rate $d{\Gamma }_{\gamma }^T/d\omega$ (for the case $\overrightarrow{k}\parallel B$), weighted in units of $\mathcal{N}\frac{e^2}{4\pi }$, at different dimensionless magnetic fields corresponding to Fig. 1.

Figure 4

D4/D6 model: photoproduction rates $d{\Gamma }_{\gamma }^y/d\omega$ and $d{\Gamma }_{\gamma }^z/d\omega$ (for the case $\overrightarrow{k}\perp B$), weighted in units of $\mathcal{N}\frac{e^2}{4\pi }$, at different dimensionless magnetic fields corresponding to Fig. 2.

Figure 5

D4/D6 model: real part of the ac conductivity along the $x$ direction at different magnetic fields corresponding to Fig. 2.

Figure 6

D4/D6 model: real part of the ac conductivity along the $z$ direction corresponding to different magnetic fields as in Fig. 5.

Figure 7

D3/D7 model: trace of the spectral function for lightlike momenta divided by frequency, ${\eta }^{\mu \nu }{\chi }_{\mu \nu }(q=\omega )/\omega$, in units of $\mathcal{N}$, for the case $\overrightarrow{k}\parallel B$. Different curves correspond to different dimensionless magnetic fields as in Fig. 1.

Figure 8

D3/D7 model: trace of the spectral function for lightlike momenta divided by frequency, ${\eta }^{\mu \nu }{\chi }_{\mu \nu }(q=\omega )/\omega$, in units of $\mathcal{N}$, for the case $\overrightarrow{k}\perp B$. Different curves correspond to different dimensionless magnetic fields as in Fig. 2.

Figure 9

D3/D7 model: photoproduction rate $d{\Gamma }_{\gamma }^T/d\omega$ (for the case $\overrightarrow{k}\parallel B$), weighted in units of $\mathcal{N}\frac{e^2}{4\pi }$, at different dimensionless magnetic fields corresponding to Fig. 1.

Figure 10

D3/D7 model: photoproduction rates $d{\Gamma }_{\gamma }^y/d\omega$ and $d{\Gamma }_{\gamma }^z/d\omega$ (for the case $\overrightarrow{k}\perp B$), weighted in units of $\mathcal{N}\frac{e^2}{4\pi }$, at different dimensionless magnetic field corresponding to Fig. 2.

Figure 11

D3/D7 model: real part of the ac conductivity along the $x$ direction at different magnetic fields as in Fig. 2.

Figure 12

D3/D7 model: real part of the ac conductivity along the $z$ direction at different magnetic fields as in Fig. 2.