Abelian projections of the mass-deformed ABJM theory and weakly curved dual geometry

Abstract

We construct N=2, 4 supersymmetric Abelian projections of the N=6 mass-deformed Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. There are well-defined dual background geometries for the N=2 Abelian theory, while those geometries are unclear for the N=4 Abelian theory. The 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 Zk 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. © 2013 American Physical Society.