Chiral transition in the probe approximation from an Einstein-Maxwell-dilaton gravity model

We refine an earlier introduced 5-dimensional gravity solution capable of holographically capturing several qualitative aspects of (lattice) QCD in a strong magnetic background such as the anisotropic behavior of the string tension, inverse catalysis at the level of the deconfinement transition or sensitivity of the entanglement entropy to the latter. Here, we consistently modify our solution of the considered Einstein-Maxwell-dilaton system to not only overcome an unphysical flattening at large distances in the quark-antiquark potential plaguing earlier work, but also to encapsulate inverse catalysis for the chiral transition in the probe approximation. This brings our dynamical holographic QCD model yet again closer to a stage at which it can be used to predict magnetic QCD quantities not directly computable via lattice techniques.

Figure 1

Deconfinement transition temperature in terms of magnetic field for the case $A_1(z)=-a{z}^2$. Here we set $\mu =0$. In units GeV.

Figure 2

Deconfinement transition temperature in terms of magnetic field for the case $A(z)=-a{z}^2-d{B}^2{z}^5$. Here we set $\mu =0$. In units GeV.

Figure 3

Deconfinement transition temperature in terms of magnetic field for the case $A(z)=-a{z}^2-d{B}^2{z}^5$. Here we set $\mu =0$. In units GeV.

Figure 4

The connected free energy ${\mathcal{F}}_{\mathrm{con}}^{\parallel }$ as a function of separation length ${\ell }^{\parallel }$ in the thermal-AdS background for the case when the Wilson loop is parallel to $\overrightarrow{B}$. Here $\mu =0$, and red, green, blue, brown, and orange curves correspond to $B=0$, 0.2, 0.4, 0.6, and 0.8 respectively. In units GeV.

Figure 5

The connected free energy ${\mathcal{F}}_{\mathrm{con}}^{\perp }$ as a function of separation length ${\ell }^{\perp }$ in the thermal-AdS background for the case when the Wilson loop is perpendicular to $\overrightarrow{B}$. Here $\mu =0$, and red, green, blue, brown, and orange curves correspond to $B=0$, 0.2, 0.4, 0.6, and 0.8 respectively. In units GeV.

Figure 6

The string tension in the parallel direction (${\sigma }_s^{\parallel }$) as a function of $B$ in the thermal-AdS background with $\mu =0$. In units GeV.

Figure 7

The string tension in the perpendicular direction ${\sigma }_s^{\perp }$ as a function of $B$ in the thermal-AdS background with $\mu =0$. In units GeV.

Figure 8

$\mathrm{\Delta }\sigma (B,T=0)=\sigma (B,T=0)-\sigma (B=0,T=0)$ as a function of magnetic field $B$ in the confined phase for the case $A_1(z)=-a{z}^2$. Here a quark mass $m_q=1.0\mathrm{GeV}$ is used.

Figure 9

$\mathrm{\Delta }\sigma (B,T)=\sigma (B,T)-\sigma (B=0,T=0)$ as a function of temperature $T$ in the deconfined phase for the case $A_1(z)=-a{z}^2$ for different values of the magnetic field. Here a quark mass $m_q=1.0\mathrm{GeV}$ is used. In units GeV.

Figure 10

$\mathrm{\Delta }\sigma (B,T)=\sigma (B,T)-\sigma (B=0,T=0)$ as a function of temperature $T$ near the inflection point in the deconfined phase for the case $A_1(z)=-a{z}^2$. Here $B=0.3$ and a quark mass $m_q=1.0\mathrm{GeV}$ are used. In units GeV.

Figure 11

Variation of the chiral critical temperature with respect to the magnetic field $B$ for the case $A_1(z)=-a{z}^2$. Here $m_q=1.0$ is used. In units GeV.

Figure 12

Variation of the chiral critical temperature, deconfinement critical temperature and $T_{\min }$ with respect to the magnetic field $B$ for the case $A_1(z)=-a{z}^2$. In units GeV.

Figure 13

$\mathrm{\Delta }\sigma (B,T=0)=\sigma (B,T=0)-\sigma (B=0,T=0)$ as a function of magnetic field $B$ in the confined phase for the case $A_2(z)=-a{z}^2-d{B}^2{z}^5$. Here a quark mass $m_q=1.0$ is used. In units of GeV.

Figure 14

$\mathrm{\Delta }\sigma (B,T)=\sigma (B,T)-\sigma (B=0,T=0)$ as a function of temperature $T$ in the deconfined phase for the case $A_2(z)=-a{z}^2-d{B}^2{z}^5$ for different values of the magnetic field. Here a quark mass $m_q=1.0$ is used. In units GeV.

Figure 15

The profile of $\mathrm{\Delta }\sigma (B,T)=\sigma (B,T)-\sigma (B=0,T=0)$ as a function of temperature $T$ near the inflection point in the deconfined phase for the case $A_2(z)=-a{z}^2-d{B}^2{z}^5$. Here $B=0.4$ and a quark mass $m_q=1.0$ are used. In units GeV.

Figure 16

Variation of the chiral critical temperature with respect to the magnetic field $B$ for the case $A_2(z)=-a{z}^2-d{B}^2{z}^5$. Here $m_q=1.0$ is used. In units GeV.

Figure 17

Variation of the chiral critical temperature, deconfinement critical temperature and $T_{\min }$ with respect to the magnetic field $B$ for the case $A_2(z)=-a{z}^2-d{B}^2{z}^5$. In units GeV.

Figure 18

The variation of potential as a function of $\varphi$ for different $z_h$. Here and $B=0.3$ is considered. Here red, green, and blue curves correspond to $z_h=0.5$, 1.0 and 1.5 respectively.

Figure 19

The variation of potential as a function of $\varphi$ for different $z_h$. Here and $B=0.5$ is considered. Here red, green, and blue curves correspond to $z_h=0.5$, 1.0, and 1.5 respectively.

Figure 20

The variation of potential as a function of $\varphi$ for different $B$. Here and $z_h=1.0$ is considered. Here red, green, blue, brown and orange curves correspond to $B=0.1$, 0.2, 0.3, 0.4, and 0.5 respectively.

Figure 21

The variation of potential as a function of $\varphi$ for different $B$. Here and $z_h=1.5$ is considered. Here red, green, blue, brown, and orange curves correspond to $B=0.1$, 0.2, 0.3, 0.4, and 0.5 respectively.

Figure 22

$\mathrm{\Delta }\sigma (B,T=0)=\sigma (B,T=0)-\sigma (B=0,T=0)$ as a function of magnetic field $B$ in the confined phase for the case $A_1(z)=-a{z}^2$. Here a quark mass $m_q=1.0$ is used. In units of GeV.

Figure 23

$\mathrm{\Delta }\sigma (B,T)=\sigma (B,T)-\sigma (B=0,T=0)$ as a function of temperature $T$ in the deconfined phase for the case $A_1(z)=-a{z}^2$ for different values of the magnetic field. Here a quark mass $m_q=1.0$ is used. In units of GeV.