Hydrodynamics, Anomaly Inflow and Bosonic Effective Field Theory

Euler hydrodynamics of perfect fluids can be viewed as an effective bosonicfield theory. In cases when the underlying microscopic system involves Diracfermions, the quantum anomalies should be properly described. In 1+1 dimensionsthe action formulation of hydrodynamics at zero temperature is reconsidered andshown to be equal to standard field-theory bosonization. Furthermore, it can bederived from a topological gauge theory in one extra dimension, whichidentifies the fluid variables through the anomaly inflow relations. Extendingthis framework to 3+1 dimensions yields an effective field theory/hydrodynamicsmodel, capable of elucidating the mixed axial-vector and axial-gravitationalanomalies of Dirac fermions. This formulation provides a platform forbosonization in higher dimensions. Moreover, the connection with 4+1dimensional topological theories suggests some generalizations of fluiddynamics involving additional degrees of freedom.