THE ABELIAN HIGGS SUNSPOT ENDOWED WITH A LOCAL CONFORMAL SYMMETRY

We show that the requirement of a local 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.