Supergravity solutions on AdS3,4,5,6,7 and the AdS/CFT correspondence

Abstract

The AdS/CFT conjecture states an equivalence between a theory of quantum gravity and a theory without gravity. It relates complementary regimes of the coupling constant of the dual pair and has been exhaustively investigated since its birth. A key tool, but not the only one, is symmetry. As we will see, there is a match between the symmetries of the two theories. We can say that this thesis is the union of two projects with the same goals, but working in different geometries. Both projects are focused on the spin-2 field perturbation of either type IIA or IIB families of 10-dimensional supergravity solutions. The perturbation of the metric is particularly interesting because of its universality. In the first project, the metric has an AdS3 factor. In the second one, we have five families and each of them has an AdS factor: AdS2, AdS4, AdS5, AdS6, and AdS7. The “first project”, the one on AdS3 × 𝑀7, is interesting from the point of view of AdS/CFT correspondence because it is dual to a 𝑑 = 2 CFT, which, in turn, possesses an infinite number of symmetry generators. In the last few years, new important examples of such correspondence were constructed in the papers [1], [2] and [3]. In this thesis, we will investigate less supersymmetric solutions. We will study the KaluzaKlein spectrum of the spin two fluctuation which is dual to the stress-energy tensor according to the conjecture. In the “second project” we investigate five families at once and show that all of them admit a certain combination of the warp factors as a solution. Such combination together with the respective spectra we call universal minimal solution.