Conformal Symmetry in Momentum Space and Anomaly Actions in Gravity

Abstract: In this thesis we study the momentum space approach to the solution of the CWI's of CFT's in higher dimensions. Our work's goal is to illustrate the essential steps needed to build tensor correlators starting from the scalar solutions, for 3-point functions. In the case of 4-point functions, our attention is centred around scalar correlators for which the CWI's are sufficient to isolate the unique solution if we enhance the symmetry with the addition of a dual conformal symmetry. Dual conformal symmetry in momentum space is obtained once the momentum variables are rewritten in a dual form, as the difference of coordinate-like variables and treated as ordinary correlators in such variables, mirroring the action of coordinate space. This enhancement of the symmetry is sufficient to fix the solutions also for such correlators. The solution of the conformal constraints are given in terms of triple-$K$ integrals and are expressed in terms of a set of constants, specific for each correlator and spacetime dimension. We present a discussion of the intermediate steps in the description of two nontrivial correlators, the $TTO$ and the $TTT$, in a more pedagogical way, offering details that could help extend such methods to higher point function.