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A<sc>bstract</sc> Euler hydrodynamics of perfect fluids can be viewed as an effective bosonic field theory. In cases when the underlying microscopic system involves Dirac fermions, the quantum anomalies should be properly described. In 1+1 dimensions the action formulation of hydrodynamics at zero temperature is reconsidered and shown to be equal to standard field-theory bosonization. Furthermore, it can be derived from a topological gauge theory in one extra dimension, which identifies the fluid variables through the anomaly inflow relations. Extending this framework to 3+1 dimensions yields an effective field theory/hydrodynamics model, capable of elucidating the mixed axial-vector and axial-gravitational anomalies of Dirac fermions. This formulation provides a platform for bosonization in higher dimensions. Moreover, the connection with 4+1 dimensional topological theories suggests some generalizations of fluid dynamics involving additional degrees of freedom. 

Abstract We study flows of barotropic perfect fluid under the simultaneous action of the electromagnetic field and the axial–vector potential, the external field conjugate to the fluid helicity. We obtain the deformation of the Euler equation by the axial–vector potential and the deformations of various currents by two external fields. We show that the divergence of the vector and axial currents are controlled by the chiral anomaly known in quantum field theories with Dirac fermions. We obtain these results by extending the variational principle for barotropic flows of a perfect fluid by coupling with the external axial–vector potential. 

Abstract We consider a free fermion formulation of a statistical model exhibiting a limit shape phenomenon. The model is shown to have a phase transition that can be visualized as the merger of two liquid regions – arctic circles. We show that the merging arctic circles provide a space-time resolved picture of the phase transition in lattice QCD known as Gross–Witten–Wadia transition. The latter is a continuous phase transition of the third order. We argue that this transition is universal and is not spoiled by interactions if parity and time-reversal symmetries are preserved. We refer to this universal transition as the merger transition. 

A bstract We show that barotropic flows of a perfect, charged, classical fluid exhibit an anomaly analogous to the chiral anomaly known in quantum field theories with Dirac fermions. A prominent effect of the chiral anomaly is the transport electric current in the fluid at equilibrium with the chiral reservoir. We find that it is also a property of celebrated Beltrami flows — stationary solutions of the Euler equation with an extensive helicity.