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

TL;DR

This paper demonstrates that the gravitational soft factor in the IR-regulated S-matrix can be fully described by boundary currents on the celestial sphere, linking IR divergences, symmetries, and memory effects.

Contribution

It reveals that the soft factor is reproduced by boundary currents related to supertranslations and their Goldstone partners, establishing a boundary current algebra structure.

Findings

Soft factor expressed via boundary currents on celestial sphere

Boundary current algebra involves supertranslations and Goldstone modes

Memory effect is an IR-safe observable within the soft S-matrix

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.