  The principal goal of the physics of the fundamental interactions is to
provide a consistent description of the nature of the subnuclear forces, which
manifest in our universe, together with the gravitational force, in a unified
framework. This attempt, which is far from being complete, is characterized by
two milestones, the Standard Model of the elementary particles and the
Einstein's theory of General Relativity. The coupling of a quantum field
theory, such as the Standard Model, to a weak gravitational background provides
significant information concerning the coupling of matter to gravity and allows
to study in a systematic way the origin of the conformal anomaly. For this
reason, the computation of correlation functions in a weak gravitational
background is of remarkable interest and the consequences of this analysis are
also of phenomenological relevance. For instance, they concern the appearance
in the spectrum of the theory of a composite state, the dilaton, which is
identified, in perturbation theory, by an infrared coupled anomaly pole. The
study of some applications of the methods discussed so far is presented in the
second part of this thesis. In particular it is shown that the analysis of the
classical metric perturbations in gravity can be related to some specific field
theories via a holographic mapping. This requires the computation of
correlators of energy-momentum tensors in $d=3$ dimensions and plays a role in
the study of the non-gaussianities of the cosmic background radiation in the
early universe. Finally, we mention an application in momentum space of the
constraints derived from the conformal symmetry in the characterization of some
correlation functions. This relies on the solution of a system of second order
partial differential equations for a certain class of generalized
hypergeometric functions of two variables.
