We construct $\mathcal{N}=2$, 4 supersymmetric Abelian projections of the $\mathcal{N}=6$ mass-deformed Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. There are well-defined dual background geometries for the $\mathcal{N}=2$ Abelian theory, while those geometries are unclear for the $\mathcal{N}=4$ Abelian theory. The $\mathcal{N}=2$ theory is built on the supersymmetric vacua of the mass-deformed ABJM theory, which are proven to have a one-to-one correspondence with the ${\mathbb{Z}}_k$ quotient of Lin-Lunin-Maldacena geometries. We select one special vacuum of the mass-deformed ABJM theory and show that the corresponding geometry is weakly curved at every point of the entire space transverse to the M2-branes in the large-$N$ limit.

• Received 19 February 2013

DOI:https://doi.org/10.1103/PhysRevD.87.085011