In this thesis we study some theoretical and phenomenological aspects of classical conformal symmetry in specific extensions of the SM. We consider both supersymmetric and non supersymmetric cases. We discuss the perturbative structure of the superconformal anomaly effective action. We show that the manifestation of the anomaly is in the presence of massless intermediate states in correlators involving the Ferrara-Zumino supercurrent with two vector supercurrents. This universal feature is typical both of chiral and conformal anomalies. These results are used in a study of a possible extension of the SM with a dilaton, deriving some bounds on a possible conformal scale. Then we turn to investigate a specific superconformal theory, the TNMSSM, which extends the MSSM with one extra triplet and a scalar singlet superfield. The manifestation of the classical conformal symmetry in this model is in the existence of a very light pseudoscalar in the physical spectrum. We study the main proprieties of this state and its potential discovery at the LHC. In the last part of this work we discuss an application of the graviton-photon-photon vertex to gravitational lensing for a Schwarzschild background. In particular, we introduce the notion of a semiclassical lens equation for the deflection of a photon nearing the horizon of a black hole.
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