Monopoles, noncommutative gauge theories in the BPS limit and some simple gauge groups

For three conspicuous gauge groups, namely, SU(2), SU(3) and SO(5), and atfirst order in the noncommutative parameter matrix h\theta^{\mu\nu}, weconstruct smooth monopole --and, some two-monopole-- fields that solve thenoncommutative Yang-Mills-Higgs equations in the BPS limit and that are formalpower series in h\theta^{\mu\nu}. We show that there exist noncommutative BPS(multi-)monopole field configurations that are formal power series inh\theta^{\mu\nu} if, and only if, two a priori free parameters of theSeiberg-Witten map take very specific values. These parameters, that are notassociated to field redefinitions nor to gauge transformations, have thusvalues that give rise to sharp physical effects.Comment: 30 pages, no figure