Vortex-type solutions in ABJM theory

We review our recent investigations on vortex type-solutions in ABJM theory without and with mass deformation. By imposing suitable supersymmetric conditions, we obtain vortex-type half-BPS equations and also its energy bound. For the undeformed ABJM theory, the resulting half-BPS equation is the same as that in SYM theory. For the mass-deformed ABJM theory, the half-BPS equations for U(2)×U(2) case reduce to the vortex equation in Maxwell-Higgs theory, which supports static regular multi-vortex solutions. In U(N)×U(N) case with N > 2 we obtain the nonabelian vortex equation of Yang-Mills-Higgs theory with a suitable ansatz. We also discuss less supersymmetric cases.