Researchers extended a path-integral formulation of scattering to include gravity. They write a boundary partition function on the lightlike boundary of spacetime (null infinity). The partition function is invariant under asymptotic symmetries. That invariance gives identities for boundary correlators that map directly to standard S-matrix statements about scattering. In particular, the work reproduces the leading and subleading soft graviton theorems from symmetry arguments.

Concretely, the authors fix asymptotic boundary conditions for the metric and massless matter fields at past and future null infinity. These boundary conditions pick out the positive or negative frequency parts of the fields relevant for in and out scattering. The central object is a Carrollian boundary partition function Z[Φ], a path integral as a function of those boundary data. Differentiating Z[Φ] produces boundary correlators (sometimes called Carrollian correlators), and after Fourier transform these correlators are identified with ordinary momentum-space S-matrix elements. The work is done perturbatively around flat (Minkowski) space and is developed at tree level.

The symmetry side uses the extended Bondi–Metzner–Sachs (BMS) group of asymptotic transformations. This group contains supertranslations (angle-dependent time shifts) and superrotations (angle-dependent rotations). Invariance of the partition function under these transformations implies Ward identities — symmetry constraints on the boundary correlators. When translated into momentum space, those Ward identities reproduce the known soft graviton theorems, which are rules that relate amplitudes with an extra very-low-energy graviton to amplitudes without it.