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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 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.