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The Soft $\mathcal{S}$-Matrix in Gravity

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arxiv 2005.13433 v2 pith:LEEWBKET submitted 2020-05-27 hep-th

classification hep-th
keywords softcurrentgravitationalmathcalmatrixcutofffactorsupertranslations
verification ladder T0 review T1 audit T2 compute T3 formal
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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.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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    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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