The abelian higgs sunspot endowed with a local conformal symmetry

We show that the requirement of alocal conformal symmetry of the Abelian Higgs sunspot leads, at least formally, to a complex-valued electromagnetic potential, whose imaginary part is a conformal compensating potential. It is shown that there exists a fundamental difference between conformal and ordinary electromagnetic fields; whereas the ordinary total magnetic flux of a spot is quantized its conformal analogue has to vanish if the Higgs field is to be single-valued. We further stress that such a complex-valued Abelian Higgs field configuration mimics quite well, under certain conditions (all the salient features of) the classical Abelian Higgs sunspot.