• AdS
• AdS/CFT
• CFT
• conformal block decomposition
• conformal field theory
• Lorentzian inversion formula
• SCFT

In this thesis we focused on studying the spectrum of a particular theory of supergravity on AdS3 × S3, that emerge from a type IIB string theory compactified on AdS3 × S3 × K3. Thanks to the so called AdS/CFT correspondence (or duality) one can relate theories of quantum gravity in d + 1 dimensions and non-gravitational QFTs on the d-dimensional boundary. In particular we use the AdS/CFT correspondence to relate the string theory compactified on AdS3 × S3 × K3 to a 2d CFT with N = (4,4) supersymmetry. We study this duality in the case of large central charge (pure SUGRA), that correspond to large N in the CFT. In particular our analysis will be at tree-level order (1/c). In this thesis we study 4-pt correlation functions of particular 1/2-BPS supermultiplets of the theory. In order to analyze these correlation functions in CFT we have the conformal block decomposition.
At this point our job will be to derive these OPE coefficients. Our approach is purely analytic and uses a formula recently found, called Lorentzian inversion formula. This formula allows us to extract the various OPE coefficients of the theory. Moreover particular non-protected operators called double-traces emerge in the theory, and acquire anomalous dimensions, that we can extract using the Lorentzian inversion formula.
In this thesis we calculate anomalous dimension of certain double-trace operators, and we compared some results with the literature.