The soft $$ \mathcal{S} $$-matrix in gravity

Abstract

The gravitational $$ \mathcal{S} $$ 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 $$ \mathcal{S} $$ S -matrix.

The structure of IR divergences in celestial gluon amplitudes

“…that has, in fact, already appeared in [84,85] for electrons and gravitons, respectively. In the next section we focus on the factorization (2.10) and we reveal the role of (2.11) in the case of celestial BDS amplitudes.…”

“…Another interesting aspect has been emphasized in [85] for graviton amplitudes. They have shown that there is a link between the resummation of IR divergences in graviton amplitudes and memory effects.…”

Coadjoint representation of the BMS group on celestial Riemann surfaces

“…On each of these surfaces, the superrotation part of the extended algebra is given by the Witt algebra only if there are two particles/punctures. In this context, complementary aspects of the BMS group have been discussed in [75][76][77][78][79][80][81][82][83][84][85][86][87][88][89][90][91][92][93].…”

Charge algebra in Al(A)dSn spacetimes

“…From these considerations, it seems to us that investigating holography in AdS with a dissipative system coupling to an environment would be a excellent starting point to apprehend flat holography in d > 2. More specifically, it would be interesting to understand how the recent advances in the celestial sphere CFT description [125][126][127][128][129][130][131][132][133][134][135][136][137][138][139] are related to the AdS results through a flat limit process.…”