AdS/CFT with tri-Sasakian manifolds

We consider generic toric tri-Sasakian 7-manifolds X7 in the context of M-theory on AdS4×X7 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.