Anomalous Hydrodynamics and Magnetohydrodynamics

Our goal is to examine the role of anomalies in the hydrodynamic regime of field theories. We employ methods based on gauge/gravity duality to examine R-charge anomalies in the hydrodynamic regime of strongly t'Hooft coupled, large $N$, $\mathcal{N}=$ 4 SYM. We use a quasiparticle treatment based on the familiar ``level-crossing" picture of chiral anomalies to investigate thermalized massless QED. In each case we find the same result. Regardless of whether a particular current is anomalously non-conserved or not, as long as it participates in an anomalous 3-pt. correlator, its constitutive relation recieves a new term: \(\vec{j}^{a} \propto - d^{abc}\vec{B}^{b}\rho^{c}\). We include a general argument for the presence of such terms, based on the formulation of hydrodynamics as an effective classical field theory.