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We explore a formulation of a perfect fluid in $3+1$ dimensions in terms of the Kalb–Ramond field. This was proposed long ago by Nambu and one of the present authors. In this note, we refine the statements in a more explicit form. We also comment on the duality with the Gross–Pitaevsky formulation written by a complex scalar field.

Note on a description of a perfect fluid by the Kalb–Ramond field