The Chern-Simons diffusion rate in strongly coupled N=4 SYM plasma in an external magnetic field

We calculate the Chern-Simons diffusion rate in a strongly coupled N=4 SUSY Yang-Mills plasma in the presence of a constant external $U(1)_R$ magnetic flux via the holographic correspondence. Due to the strong interactions between the charged fields and non-Abelian gauge fields, the external Abelian magnetic field affects the thermal Yang-Mills dynamics and increases the diffusion rate, regardless of its strength. We obtain the analytic results for the Chern-Simons diffusion rate both in the weak and strong magnetic field limits. In the latter limit, we show that the diffusion rate scales as $B\times T^2$ and this can be understood as a result of a dynamical dimensional reduction.