From the AdS/CFT Correspondence to Celestial Correlation Functions

Throughout history there have been numerous attempts to unify relativity, gravitation and quantum mechanics. An area of physics that is not yet completely clear and on which research is still developing is quantum gravity, the theory that would unify quantum field theory and general relativity. There are no local observables in quantum gravity, suggesting that they live on the boundary at infinity i.e. that they are holographic in nature. An area of current research applies mathematical consistency to constrain high energy physics theories, which is an idea known as the Bootstrap. The Bootstrap is especially powerful in special types of quantum field theories known as Conformal Field Theories (CFT). The most important application of CFT is that they are conjectured to be equivalent to theories of quantum gravity that live in Anti de Sitter (AdS) space of one higher dimension, which is a maximally symmetric space with a constant negative curvature. This duality is known as the "AdS/CFT correspondence". It is imperative to extend these successes of the AdS/CFT to scenarios closer to that of our own universe and in this thesis this has been explored for theories in Minkowski space, known as Celestial Holography, where boundary observables are formulated on what is known as the celestial sphere at null infinity. In particular, it has been shown that holographic correlators on the celestial sphere can be perturbatively re-cast in terms of boundary correlators in AdS space, opening up the possibility to import understanding from the relatively well understood AdS/CFT correspondence. The last two chapters consist of my personal contribution to this line of research, where the consequences of this relationship are explored for models of physical interest such as massless particles (as a toy model for massless particles with spin e.g. photon and graviton) and Fermions which describe matter particles in the Standard Model of Particle Physics.