Comment on "Energy Transfer and Dual Cascade in Kinetic Magnetized Plasma Turbulence"

We argue that the constraints on transfers, given in the Letter [G. Plunk and T. Tatsuno, Phys. Rev. Lett. {\bf 106}, 165003 (2011)], but not correctly, do not give the transfer and/or cascade directions which however can be assisted by the absolute equilibria calculated in this Comment, following Kraichnan [R. H. Kraichnan, Phys. Fluids {\bf 102}, 1417 (1967)]. One of the important statements about the transfers with only one or no diagonal component can be shown to be inappropriate according to the fundamental dynamics. Some mathematical mistakes are pointed out.