Moduli space metric of the excited vortex

Abstract: We show that the moduli space metric of a single vortex gets corrections because of the excitation of the radially symmetric shape mode. It leads to a non-zero amount of the shape mode carried by the vortex when moving with a constant velocity. However, due to the radial symmetry, this effect does not reproduce the Lorentz contraction of the moving vortex. We apply the Derrick mode approximation in order to recover the Lorentz contraction on the level of the collective model.