Strings, superfluid vortices, and relativity.

Abstract

The domain of validity of the harmonicity assumption for global strings (i.e., the assumption that the Goldstone boson is a free massless field) and the related incompressibility assumption for an irrotational flow with isolated vortices (which include superfluid vortices as a particular case) are investigated in a combined Lorentz-covariant model. A modification of the Kalb-Ramond interstring interaction which does not take these assumptions into account is developed, and first-order corrections to the Kalb-Ramond fields are calculated. These corrections are found to be of the order of ${(\mathrm{c}\mathrm{o}\mathrm{r}\mathrm{e}\phantom{\rule{0ex}{0ex}}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{u}\mathrm{s}/\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{o}\mathrm{r}\mathrm{t}\mathrm{e}\mathrm{x}\phantom{\rule{0ex}{0ex}}\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e})}^{2}$, implying that they are expected to be significant in understanding vortex creation and the intercommuting of vortices. The corrections are also interpreted as inducing vorticity in the medium in which the vortices appear, including in the vacuum in which global strings appear.