We study Aharony-Bergman-Jafferis-Maldacena (ABJM) theory without and with
mass deformation. It is shown that maximally supersymmetry preserving, D-term,
and F-term mass deformations of single mass parameter are equivalent. We obtain
vortex-type half-BPS equations and the corresponding energy bound. For the
undeformed ABJM theory, the resulting half-BPS equation is the same as that in
supersymmetric Yang-Mills theory and no finite energy regular BPS solution is
found. For the mass-deformed ABJM theory, the half-BPS equations for U(2)xU(2)
case reduce to the vortex equation in Maxwell-Higgs theory, which supports
static regular multi-vortex solutions. In U(N)xU(N) case with N>2 the
nonabelian vortex equation of Yang-Mills-Higgs theory is obtained.Comment: 22 pages, v2: references added, v3: minor correction, to appear in
PR