Holographic chiral electric separation effect

We investigate the chiral electric separation effect, where an axial current is induced by an electric field in the presence of both vector and axial chemical potentials, in a strongly coupled plasma via the Sakai-Sugimoto model with a $U(1{)}_R\times U(1{)}_L$ symmetry. By introducing different chemical potentials in $U(1{)}_R$ and $U(1{)}_L$ sectors, we compute the axial direct current (DC) conductivity stemming from the chiral current and the normal DC conductivity. We find that the axial conductivity is approximately proportional to the product of the axial and vector chemical potentials for arbitrary magnitudes of the chemical potentials. We also evaluate the axial alternating current (AC) conductivity induced by a frequency-dependent electric field, where the oscillatory behavior with respect to the frequency is observed.

Figure 1

The DC conductivities in the $L/R$ bases versus the chemical potentials scaled by temperature.

Figure 2

The blue and red(dashed) curves correspond to the normal DC conductivity and the axial one with ${\mu }_V=T$, respectively.

Figure 3

The blue and red(dashed) curves correspond to the normal DC conductivity and the axial one with ${\mu }_A=0.5T$, respectively.

Figure 4

Power-counting estimation in (12) with ${\mu }_A=0.01T$.

Figure 5

Power-counting estimation in (12) with ${\mu }_V=0.2T$.

Figure 6

The red, blue(dashed), and black(dot-dashed) curves correspond to the cases with ${\mu }_V=T$, $0.6T$, and 0, $3T$. Here ${\widehat{\mu }}_{V/A}={\mu }_{V/A}/T$.

Figure 7

The red(solid), blue(dashed), and green(dotted) curves correspond to the real part of the normal AC conductivity with ${\mu }_A=0.2T$, $0.5T$, and $0.9T$, respectively. Here ${\mu }_V=T$.

Figure 8

The red(solid), blue(dashed), and green(dotted) curves correspond to the real part of the axial AC conductivity with ${\mu }_A=0.2T$, $0.5T$, and $0.9T$, respectively. Here ${\mu }_V=T$.

Figure 9

The red(solid), blue(dashed), and green(dotted) curves correspond to the imaginary part of the axial AC conductivity with ${\mu }_A=0.2T$, $0.5T$, and $0.9T$, respectively. Here ${\mu }_V=T$.

Figure 10

The DC conductivities in the $L/R$ bases versus the chemical potentials scaled by temperature. The dashed red curve and solid blue curve correspond to the result from the background-field expansion and from solving the full DBI action, respectively.

Figure 11

The blue and red(dashed) curves correspond to the normal DC conductivity and the axial one with ${\mu }_V=4T$, respectively.

Figure 12

The blue and red(dashed) curves correspond to the normal DC conductivity and the axial one with ${\mu }_A=3T$, respectively.

Figure 13

The red, blue(dashed), black(dot-dashed), and green(long-dashed) curves correspond to the cases with ${\mu }_V=10T$, $8T$, $4T$, and $T$. Here ${\widehat{\mu }}_{V/A}={\mu }_{V/A}/T$.

Figure 14

The green(solid), red(long-dashed), and black(dot-dashed) curves correspond to the real part of the normal AC conductivity with $({\mu }_V,{\mu }_A)=(4T,3T)$, $(4T,T)$ and $(T,0.9T)$. The blue(dashed) curve corresponds to the one with $({\mu }_V,{\mu }_A)=(T,0.9T)$ from the background-field expansions.

Figure 15

The real part of the axial AC conductivity with the colors corresponding to the same cases as Fig. 14.

Figure 16

The imaginary part of the axial AC conductivity with the colors corresponding to the same cases as Fig. 14.