  Some quantum features of vortices in supersymmetric theories in 1+2
dimensions are studied in a manifestly supersymmetric setting of the superfield
formalism. A close examination of the supercurrent that accommodates the
central charge and super-Poincare charges in a supermultiplet reveals that
there is no genuine quantum anomaly in the supertrace identity and in the
supercharge algebra, with the central-charge operator given by the bare
Fayet-Iliopoulos term alone. The central charge and the vortex spectrum undergo
renormalization on taking the expectation value of the central-charge operator.
It is shown that the vortex spectrum is exactly determined at one loop while
the spectrum of the elementary excitations receives higher-order corrections.
