Abstract
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 in [1, 2]. 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.
Highlights
For zero-temperature superfluids the only allowed vortex configurations are string-like objects, the so-called vortex lines
For ordinary fluids one can have much more general vortex configurations, but it is still possible to set up a long-lived string-like vortex, with a thickness that is much smaller than its other typical length scales
The position and shape of a vortex line is a placeholder for a fairly complicated bulk fluid flow: vorticity is localized on the line, but the velocity field away from it is non-trivial
Summary
For zero-temperature superfluids the only allowed vortex configurations are string-like objects, the so-called vortex lines. For ordinary fluids one can have much more general vortex configurations, but it is still possible (and fairly easy) to set up a long-lived string-like vortex, with a thickness that is much smaller than its other typical length scales In both cases, the position and shape of a vortex line is a placeholder for a fairly complicated bulk fluid flow: vorticity is localized on the line, but the velocity field away from it is non-trivial (albeit irrotational). The classic logarithms appearing in a number of physical quantities concerning vortex lines [4, 16] — from their energy per unit length to the spectrum of Kelvin waves — can be understood in this way Such logarithmic running at the classical level arises quite generally when the dynamics of a codimension-two brane — which in our case is just the worldsheet spanned by the vortex line — couples to fields in the bulk [17, 18].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
