TOPOLOGICAL INVARIANCE OF FRACTIONAL SPIN OF THE ABELIAN CSH VORTEX

The Abelian Chern-Simons-Higgs model in 2 + 1 dimensions exhibit vorte x solutions with fractional spin. Although it is known that the normal , underformed charged vortex has a fractional spin related to its topo logical charge, it is not clear whether the value of this fractional s pin is stable under changes in gauge-fixing conditions and regular def ormations of the vortex field configurations. Recently, some authors h ave reported about the gauge as well as shape dependence of the fracti onal spin for the CSH vortex, which is contrary to our usual belief. H owever, their analysis is inconsistent and calls for a careful scrutin y. An explicit analysis is presented in this paper to show that the fr actional spin for the Abelian CSH charged vortex may indeed be taken t o be a gauge (small) and shape independent and hence, a topologically invariant quantity. The subtle points missed out by the other authors leading to inconsistency and the contradictory result are discussed in all essential details to resolve the issue.