Supergravity, AdS/CFT Correspondence and Conformal Bootstrap

We study the SO(3)D x SO(3)L sector of both the SO(8) and ISO(7) gauged N = 8 supergravity in four dimensions. By uplifting an N = 3 critical point of the latter theory, we get a wrapped AdS4 x M6 in ten dimensional massive type IIA supergravity. The dual three dimensional superconformal Chern-Simons theory is identified through AdS/CFT correspondence. The conjecture is tested by comparing the spin-2 Kaluza-Klein modes and spin-2 operators in the dual CFT, and by comparing the Gravitional Euclidean Action of the gravitational solution and Free Energy of the dual CFT. We review the non-perturbative method to study conformal field theory called “Conformal Bootstrap" and apply it to study CFT's with F4/SU(3) flavor symmetry in 6 - ϵ dimensions. The possibility of applying conformal bootstrap to study AdS/CFT is also discussed