Aspects of Symmetry in Asymptotically Flat Spacetimes
Kapec, Daniel Steven
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AbstractWe explore the nature and implications of a variety of asymptotic symmetry groups associated to gauge theory and quantum gravity in asymptotically flat spacetimes. We re-express Weinberg's soft graviton theorem as a Ward identity for supertranslation invariance of the gravitational S-matrix, and provide an alternate derivation of these symmetries as nontrivial large diffeomorphisms preserving finite-energy boundary conditions at null infinity. Similarly, we recast Weinberg's soft photon theorem as a Ward identity for infinitely many new symmetries of the massless QED S-matrix. These symmetries are identified as large gauge transformations with angle-dependent gauge parameters, and lead to a degeneracy of the gauge theory vacuum. We then extend the analysis to incorporate massive charged particles. Transitions among the degenerate vacua are induced in any nontrivial scattering process, but conventional computations of scattering amplitudes in QED ignore this fact and therefore always give zero due to infrared divergences. We demonstrate that if these vacuum transitions are properly accounted for, the resulting amplitudes are nonzero and infrared finite.
We then utilize the subleading soft graviton theorem to demonstrate that the S-matrix for quantum gravity in four-dimensional Minkowski space has a Virasoro symmetry which acts on the celestial sphere at null infinity. We construct an operator T whose insertion in the four-dimensional S-matrix obeys the Ward identities of the energy-momentum tensor of a two-dimensional CFT. Generalizing to higher dimensions, the (d+2)-dimensional S-matrix elements are recast as correlation functions of local operators living on a spacelike cut M of the null momentum cone. The Lorentz group SO(d+1,1) is nonlinearly realized as the Euclidean conformal group on M. We demonstrate that the leading soft photon operator is the shadow transform of a conserved spin-one primary operator J, and the subleading soft graviton operator is the shadow transform of a conserved spin-two symmetric traceless primary operator T. The universal form of the soft limits ensures that J and T obey the Ward identities expected of a conserved current and energy-momentum tensor in a Euclidean d-dimensional CFT, respectively.
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