Temperature derivative divergence of the electric conductivity and thermal photon emission rate at the critical end point from holography

The thermal photon emission rate $\frac{d\mathrm{\Gamma }}{dk}$ and DC eletric conductivity ${\sigma }_Q$ of the strongly coupled quark-gluon plasma (sQGP) are investigated around the critical end point in a $N_f=2+1$ holographic QCD model with parameters obtained from machine-learning. It is found that both thermal photon emission rate and eletric conductivity grow most obviously around $T_c$, which agrees with the previous studies, and the result of eletric conductivity at zero chemical potential resembles the lattice results. Moreover, it is found that both the temperature derivative of the eletric conductivity and thermal photon emission rate diverge at the critical end point.