Energy loss of a nonaccelerating quark moving through a strongly coupled N=4 super Yang-Mills vacuum or plasma in strong magnetic field

Abstract

Using AdS/CFT correspondence, we find that a massless quark moving at the speed of light $v=1$, in arbitrary direction, through a strongly coupled $\mathcal{N}=4$ super Yang-Mills (SYM) vacuum at $T=0$, in the presence of strong magnetic field $\mathcal{B}$, loses its energy at a rate linearly dependent on $\mathcal{B}$, i.e., $\frac{dE}{dt}=-\frac{\sqrt{\lambda}}{6\pi}\mathcal{B}$. We also show that a heavy quark of mass $M\neq 0$ moving at near the speed of light $v^2=v_{*}^2=1-\frac{4\pi^2 T^2}{\mathcal{B}}\simeq1$, in arbitrary direction, through a strongly coupled $\mathcal{N}=4$ SYM plasma at finite temperature $T\neq 0$, in the presence of strong magnetic field $\mathcal{B}\gg T^2$, loses its energy at a rate linearly dependent on $\mathcal{B}$, i.e., $\frac{dE}{dt}=-\frac{\sqrt{\lambda}}{6\pi}\mathcal{B}v_{*}^2\simeq-\frac{\sqrt{\lambda}}{6\pi}\mathcal{B}$. Moreover, we argue that, in the strong magnetic field $\mathcal{B}\gg T^2$ (IR) regime, $\mathcal{N}=4$ SYM and adjoint QCD theories (when the adjoint QCD theory has four flavors of Weyl fermions and is at its conformal IR fixed point $\lambda=\lambda^*$) have the same microscopic degrees of freedom (i.e., gluons and lowest Landau levels of Weyl fermions) even though they have quite different microscopic degrees of freedom in the UV when we consider higher Landau levels. Therefore, in the strong magnetic field $\mathcal{B}\gg T^2$ (IR) regime, the thermodynamic and hydrodynamic properties of $\mathcal{N}=4$ SYM and adjoint QCD plasmas, as well as the rates of energy loss of a quark moving through the plasmas, should be the same.