Abstract
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.
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Acknowledgments
We gratefully acknowledge P. Wiegmann for collaboration in the early stages of this work and for useful criticism. We also benefit from interesting exchanges with J. Fröhlich, F. M. Haehl, K. Jensen, B. Khesin, N. Nekrasov, N. Pinzani-Fokeeva, R. Villa, A. Yarom. A.C. would like to thank Marco Ademollo, Marcello Ciafaloni and Stefano Catani for sharing their passion for theoretical physics. The work of A.C. has been partially supported by the grant PRIN 2017 provided by the Italian Ministery of University and Research. The work of A.G.A. has been supported by the National Science Foundation under Grant NSF DMR-2116767 and by NSF-BSF grants 2020765, 2022110. A.G.A. also acknowledges the support of Rosi and Max Varon fellowship from the Weizmann Institute of Science and the hospitality of the Galileo Galilei Institute for Theoretical Physics.
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Abanov, A.G., Cappelli, A. Hydrodynamics, anomaly inflow and bosonic effective field theory. J. High Energ. Phys. 2024, 57 (2024). https://doi.org/10.1007/JHEP08(2024)057
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DOI: https://doi.org/10.1007/JHEP08(2024)057