We study the 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 $\mathrm{U}(2)\times \mathrm{U}(2)$ case reduce to the vortex equation in Maxwell-Higgs theory, which supports static regular multivortex solutions. In $\mathrm{U}(N)\times \mathrm{U}(N)$ case with $N>2$ the non-Abelian vortex equation of Yang-Mills-Higgs theory is obtained.

• Received 10 June 2009

DOI:https://doi.org/10.1103/PhysRevD.80.045013