Existence of multiple vortices in supersymmetric gauge field theory
نویسندگان
چکیده
Two sharp existence and uniqueness theorems are presented for solutions of multiple vortices arising in a six-dimensional brane-world supersymmetric gauge field theory under the general gauge symmetry group G =U (1)× SU (N ) and with N Higgs scalar fields in the fundamental representation of G. Specifically, when the space of extra dimension is compact so that vortices are hosted in a 2-torus of volume |U|, the existence of a unique multiple vortex solution representing n1, . . . ,nN , respectively, prescribed vortices arising in the N species of the Higgs fields is established under the explicitly stated necessary and sufficient condition
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