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.
Highlights
Pieces, where the soft piece is given by a universal formula that contains all IR divergences of the full amplitude
In addition to the previously-studied supertranslation current [5, 6], we find that the celestial algebra includes a second “Goldstone current” that is the gradient of the Goldstone mode associated to spontaneously broken supertranslation symmetry
Memory is an IR safe observable and we show it is reproduced in the current algebra by the IR finite operator product expansion (OPE) between the supertranslation current and Goldstone boson
Summary
We consider four-dimensional perturbative gravity coupled to massless matter on a Minkowski background. We parametrize null momenta as pμk = ηkωkqμ(zk, zk). Where ωk ≥ 0, ηk = ±1 for outgoing and incoming particles respectively, and qμ(z, z) = (1 + zz, z + z, −i(z − z), 1 − zz), qμ(zi, zi)qμ(zj, zj) = −2|zi − zj|2 ≡ −2|zij|2. The polarization tensor for a positive helicity outgoing graviton is εμk+ν = εμk+ενk+. The Minkowski line element becomes ds2 = ημνdxμdxν = −dudr + r2dzdz. In these coordinates, the celestial sphere CS is conformally mapped to a plane on which (zk, zk) labels the point where a massless particle with momentum pk crosses null infinity I
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
