It is shown that the tree-level S-matrix for quantum gravity in four-dimensional Minkowski space has a Virasoro symmetry which acts on the conformal sphere at null infinity.

The Event Horizon Telescope image of the supermassive black hole in the galaxy M87 is dominated by a bright, unresolved ring. General relativity predicts that embedded within this image lies a thin "photon ring," which is composed of an infinite sequence of self-similar subrings that are indexed by the number of photon orbits around the black hole. The subrings approach the edge of the black hole "shadow," becoming exponentially narrower but weaker with increasing orbit number, with seemingly negligible contributions from high order subrings. Here, we show that these subrings produce strong and universal signatures on long interferometric baselines. These signatures offer the possibility of precise measurements of black hole mass and spin, as well as tests of general relativity, using only a sparse interferometric array.

The soft photon theorem in U (1) gauge theories with only massless charged particles has recently been shown to be the Ward identity of an infinite-dimensional asymptotic symmetry group. This symmetry group is comprised of gauge transformations which approach angle-dependent constants at null infinity. In this paper, we extend the analysis to all U (1) theories, including those with massive charged particles such as QED.

We use the subleading soft-graviton theorem to construct an operator T_{zz} whose insertion in the four-dimensional tree-level quantum gravity S matrix obeys the Virasoro-Ward identities of the energy momentum tensor of a two-dimensional conformal field theory (CFT_{2}). The celestial sphere at Minkowskian null infinity plays the role of the Euclidean sphere of the CFT_{2}, with the Lorentz group acting as the unbroken SL(2,C) subgroup.

Recently it has been shown that the vacuum state in QED is infinitely degenerate.Moreover a transition among the degenerate vacua is induced in any nontrivial scattering process and determined from the associated soft factor. Conventional computations of scattering amplitudes in QED do not account for this vacuum degeneracy and therefore always give zero. This vanishing of all conventional QED amplitudes is usually attributed to infrared divergences. Here we show that if these vacuum transitions are properly accounted for, the resulting amplitudes are nonzero and infrared finite. Our construction of finite amplitudes is mathematically equivalent to, and amounts to a physical reinterpretation of, the 1970 construction of Faddeev and Kulish.