The anomalous effective action as an ideal fluid

The anomalous sector of QED can be described with an effective action involving two pseudoscalar degrees of freedom. We show that this action supplemented with an equilibrium energy density describes a quantum fluid. Using this EFT we show that the commutation relation originating in the corresponding Hamiltonian formalism reproduces the anomalous commutators of the current algebra. We re-derive the anomalous transport within this formalism in 4d and 2d QED. In 2d case we show that the action of this anomalous fluid is in one-to-one correspondence with the bosonized action of the Schwinger model.