A framework of connections between asymptotic symmetries, soft theorems, and memory effects has recently shed light on a universal structure associated with infrared physics. Here, we show how this pattern has been used to fill in missing elements. After the necessary groundwork, we begin by proving a Ward identity for superrotations using the subleading soft graviton theorem, thereby demonstrating a semiclassical Virasoro symmetry for scattering in quantum gravity. Next, we show there exists a new spin memory effect associated with this symmetry, explain more generally how the connections between the vertices of the infrared triangle predicted this, and describe what other examples and variations have been unveiled. Taking to heart this newly motivated Virasoro symmetry, we review how the soft theorem has been recast as a Virasoro Ward identity for a putative two dimensional conformal field theory. This derivation relies upon a map from plane wave scattering states to a conformal primary basis, which we then construct. We provide examples of familiar scattering amplitudes recast in this basis and discuss the somewhat exotic nature of the putative CFT2. We conclude by describing ongoing efforts to tame some of these features and what this change of basis in turn has taught us about the infrared limit which began our story.

PhD Thesis