Shouxin Chen, Yisong Yang. Existence of Multiple Vortices in Supersymmetric Gauge Field Theory

Natural Sciences / Physics / Mathematical Physics

Submitted on: Aug 30, 2012, 09:11:27

Description: 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 $G=U(1)times SU(N)$ 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 $|Om|$, the existence of a unique multiple vortex solution representing $n_1...,n_N$ respectively prescribed vortices arising in the $N$ species of the Higgs fields is established under the explicitly stated necessary and sufficient condition [ n_i
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