Abstract
The Abelian Chern–Simons–Higgs model in 2 + 1 dimensions exhibit vortex solutions with fractional spin. Although it is known that the normal, underformed charged vortex has a fractional spin related to its topological charge, it is not clear whether the value of this fractional spin is stable under changes in gauge-fixing conditions and regular deformations of the vortex field configurations. Recently, some authors have reported about the gauge as well as shape dependence of the fractional spin for the CSH vortex, which is contrary to our usual belief. However, their analysis is inconsistent and calls for a careful scrutiny. An explicit analysis is presented in this paper to show that the fractional spin for the Abelian CSH charged vortex may indeed be taken to 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.
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