On Soft Symmetries in Gravity and Gauge Theory

Abstract

A precise equivalence relating soft theorems, asymptotic symmetries and memory effects governs the low-energy sector of any theory with massless particles in asymptotically flat spacetimes. We study aspects of this equivalence and its implications for quantum gravity and gauge theories. First, starting from the subleading soft graviton theorem, we construct an operator $T_{zz}$ whose insertions in the four-dimensional tree-level quantum gravity $\mathcal{S}-$matrix obey the Virasoro-Ward identities of the stress tensor in a two-dimensional conformal field theory. Moreover, we find evidence that this Virasoro symmetry persists in the quantum theory upon a redefinition of the stress tensor. In quantum electrodynamics (QED) infrared divergences exponentiate and set all $\mathcal{S}-$matrix elements to zero. We next demonstrate that this is a consequence of a violation of the conservation law associated with large gauge symmetries. One way to ensure that scattering amplitudes obey the conservation law is to dress the asymptotic states by coherent clouds of soft photons. This implies that any non-trivial scattering process in QED has to be accompanied by a vacuum transition, providing a new physical interpretation for a long-known construction. Further, we start with the representation of momentum-space scattering amplitudes as correlation functions on the celestial sphere and describe various constraints the latter have to obey. We demonstrate that the leading soft theorem maps to a conformally soft theorem relating celestial amplitudes with and without insertions of certain soft currents and verify explicitly that known celestial amplitudes in gauge theory satisfy this relation. We then show that the celestial analogs of subleading and sub-subleading soft theorems in gauge theory and gravity completely determine the leading coefficients in a collinear expansion of gluons and gravitons. Finally, we study memory effects in higher even-dimensional gravity and non-abelian gauge theory. In particular, we work out the memory effect in Yang-Mills theory where a color flux through future null infinity induces a color rotation of a pair of test particles carrying color charge. We conclude with a proposal for observing this effect in the high-energy limit of quantum chromodynamics at fixed momentum transfer.