Research Projects

11d supergravity admits classical solutions of the form M_4 X M_7, where M_4 is an AdS_4 and M_7 is a compact 7d Einstein manifold with positive curvature. The compactification of 11d supergravity was of great interest in the 80s due to the emergence of the group SU(3) X SU(2) X U(1) as the symmetry group of the internal manifold M_7. Later, some of these internal manifolds were classified and found to be tri-Sasaki-Einstein (SE) manifolds, which play an important role in the context of AdS/CFT correspondence. Checks of AdS/CFT duality mostly rely on methods such as matching superconformal indices (SCI), matching moduli spaces, and comparing partition functions. The first example of a AdS_4 /CFT_3 is the ABJM theory, which admits M-theory vacua S_7 /Z_k. Many superconformal Chen-Simons (CS) theories in 3d have been constructed with N = 2,3,4 supersymmetries, having AdS_4 X M_7 vacua in M-theory. The main focus of this project is to explore non-homogeneous SE manifolds, which correspond to a class of N = 3 SCF quiver CS matter theories falling under the ADE classification. The project aims to compute the multiparticle graviton index of the conjectured gravity dual of N = 3 CS matter theories with ADE classification of the form AdS_4 X M_7.