On Soft Theorems and Asymptotic Symmetries in Four Dimensions

Abstract

It was recently discovered that soft theorems, Ward identities associated to asymptotic symmetries, and the memory effect in gravity and gauge theories are in fact mathematically equivalent. This is a rather remarkable correspondence, as each of these subjects in theoretical physics has been extensively but separately studied for many decades. Since then, this correspondence has been widely exploited to explore the infrared structure of various theories, and has been particularly fruitful both in giving new insights towards a potential holographic description of scattering amplitudes in asympototically flat spacetimes as well as possibly resolving the black hole information paradox. In this thesis, I will chronicle the early progress made in establishing the equivalence between the soft theorems and asymptotic symmetries of gravity and gauge theories in four spacetime dimensions. Specifically, I will demonstrate that the leading soft theorems in 4D quantum electrodynamics (QED), nonabelian gauge theory, N=1 supersymmetric QED, and gravity in asymptotically flat spacetimes all correspond to Ward identities of asymptotic symmetries in those theories. I will lastly use the subleading soft graviton theorem to make progress towards constructing a one-loop exact operator, whose insertion into scattering amplitudes generates the Virasoro-Ward identities associated to a energy-momentum tensor in a 2D conformal field theory.