Effective theories of vortex lines

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Vortex lines are a distinctive feature of superfluids and are characterized by a very peculiar dynamics. In this talk, I will first discuss the behavior of vortex lines in a non-relativistic superfluids in the incompressible limit. I will then introduce an effective theory of vortex lines coupled to sound which applies to relativistic superfluids. I will conclude by briefly discussing the similarities between the effective theory for vortex lines and non-relativistic General Relativity.