  A series of sharp existence and uniqueness theorems are established for the
multiple vortex solutions in the supersymmetric Chern--Simons--Higgs theory
formalism of Aharony, Bergman, Jaferis, and Maldacena, for which the Higgs
bosons and Dirac fermions lie in the bifundamental representation of the
general gauge symmetry group $U(N)\times U(N)$. The governing equations are of
the BPS type and derived by Kim, Kim, Kwon, and Nakajima in the mass-deformed
framework labeled by a continuous parameter.
