Soft Travels to the Celestial Sphere

Abstract

For decades, a prominent question in theoretical physics has been to find a theory of “quantum gravity.” Popularly referred to as the theory of everything, such a theory would simultaneously explain the four fundamental forces of nature. A promising approach is string theory which starts with a very general model and then tries to simplify it to one that describes our universe. A seemingly opposite approach is celestial holography which starts with what we know about the real world and aims to build up to a theory of quantum gravity. This relies on the equivalence between a theory of quantum gravity and a theory that is relatively easier to study, known as a “celestial” conformal field theory. The concrete map between the two theories means that if we know the complete information about one, then we know everything about the other. Therefore, our problem amounts to completely understanding the celestial theory. In this thesis we start by introducing the historical building blocks of this program which include, at the most basic level, quantum field theory and general relativity as well as the notion of asymptotically flat spaces. We discuss the symmetries of this class of spacetimes and relate them to an important feature of scattering amplitudes known as soft theorems. Using the holographic duality we recast this relationship in the context of operators that live on the boundary theory. We then discuss relevant aspects of these operators that allow us to probe various properties of our bulk theory in an attempt to construct a concrete duality.