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We discuss the effective string theory of vortex lines in ordinary fluids andlow-temperature superfluids, by describing the bulk fluid flow in terms of atwo-form field to which vortex lines can couple. We derive the most generallow-energy effective Lagrangian that is compatible with (spontaneously broken)Poincare invariance and worldsheet reparameterization invariance. Thisgeneralizes the effective action developed by Lund and Regge and by Endlich andNicolis. By applying standard field-theoretical techniques, we show thatcertain low-energy coupling constants -- most notably the string tension --exhibit RG running already at the classical level. We discuss applications ofour techniques to the study of Kelvin waves, vortex rings, and the coupling tobulk sound modes.

Effective string theory for vortex lines in fluids and superfluids