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