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The Soft $\mathcal{S}$-Matrix in Gravity
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abstract
The gravitational $\mathcal{S}$-matrix defined with an infrared (IR) cutoff factorizes into hard and soft factors. The soft factor is universal and contains all the IR and collinear divergences. Here we show, in a momentum space basis, that the intricate expression for the soft factor is fully reproduced by two boundary currents, which live on the celestial sphere. The first of these is the supertranslation current, which generates spacetime supertranslations. The second is its symplectic partner, the Goldstone current for spontaneously broken supertranslations. The current algebra has an off-diagonal level structure involving the gravitational cusp anomalous dimension and the logarithm of the IR cutoff. It is further shown that the gravitational memory effect is contained as an IR safe observable within the soft $\mathcal{S}$-matrix.
Forward citations
Cited by 5 Pith papers
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An algebra of proper observables at null infinity: Dirac brackets, Memory and Goldstone probes
The algebra of proper observables at null infinity admits Goldstone probes that measure the memory mode, but none can be built from shear or news alone, and the Dirac brackets acquire non-local corrections.
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An algebra of proper observables at null infinity: Dirac brackets, Memory and Goldstone probes
Authors define proper observables and Goldstone probes on the Ashtekar-Streubel phase space at null infinity, showing supertranslation charges act correctly on shear and deriving distributional Dirac brackets with non...
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Localization and anomalous reference frames in gravity
Constructs a phase space for gravitational degrees of freedom on null ray segments with commuting localized observables via edge modes and dressing time, then introduces an effective classical theory with Virasoro def...
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Effective density matrix for vacua in asymptotically flat gravity
The vacuum of a large causal diamond in asymptotically flat gravity is claimed to be a Gaussian in the supertranslation Goldstone mode, giving modular Hamiltonian variance A/epsilon squared.
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Lectures on Carrollian Holography
Massless scattering amplitudes, including gravitons, can be recast as correlators of a carrollian conformal field theory on null infinity, but the non-perturbative bootstrap program remains incomplete.
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