su(N) Mermin-Ho relation

Abstract: The Mermin-Ho relation expresses the vorticity of a coreless su(2) vortex in terms of the spin-1 or l vector which characterizes fully polarized superfluid textures. We generalize it to an su(N) vortex which is applicable to arbitrarily polarized superfluid textures with higher spin or angular momentum. The obtained relation is expressed in terms of the mean-field generators and their structure factors.