AdS/CFT with Tri-Sasakian Manifolds

Abstract We consider generic toric tri-Sasakian 7-manifolds X 7 in the context of M-theory on AdS 4 × X 7 and study their AdS/CFT correspondence to N = 3 SCFT in 3D space–time. We obtain volumes of tri-Sasakian manifolds and their supersymmetric 5-cycles via cohomological integration technique, and use this to calculate conformal dimensions of baryonic operators in the SCFT side. We also propose quiver-type gauge theories for UV description of the corresponding N = 3 SCFT.