Topological Landau-Ginzburg theory for vortices in superfluidHe4

We propose a modified Landau-Ginzburg theory for arbitrarily shaped vortex strings in superfluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. The theory contains a topological term and directly describes vortex dynamics. We introduce gauge fields in order to remove singularities from the Landau-Ginzburg order parameter of the superfluid, so that two kinds of gauge symmetries appear, making the continuity equation and conservation of the total vorticity manifest. The topological term gives rise to the Berry phase term in the vortex mechanical actions.