Scalar-graviton amplitudes and celestial holography

Celestial amplitudes may be decomposed as weighted integrals of AdS3-Witten diagrams associated to each leaf of a hyperbolic foliation of spacetime. We show, for the Kleinian three-point MHV amplitude, that each leaf subamplitude is smooth except for the expected light-cone singularities. Moreover, we find that the full translationally-invariant celestial amplitude is simply the residue of the pole in the leaf amplitude at the point where the total conformal weights of the gluons equals three. This full celestial amplitude vanishes up to light-cone contact terms, as required by spacetime translation invariance, and reduces to the expression previously derived by Mellin transformation of the Parke-Taylor formula.

Celestial leaf amplitudes

Melton,

Sharma,

Strominger

2024

w1+∞ in 4D gravitational scattering

Himwich,

Pate

2024

In four-dimensional asymptotically flat spacetimes, an infinite tower of soft graviton modes is known to generate the symmetry algebra of w1+∞ at tree-level. Here we demonstrate that the symmetry action follows from soft graviton theorems and acts non-trivially on massive scalar particles. By generalizing previous analyses that were specifically tailored to the scattering of massless particles, our results clarify that w1+∞ symmetry is a universal feature of tree-level gravitational scattering in four-dimensional asymptotically flat spacetimes and originates from minimally-coupled gravitational interactions. In addition, we show that the w1+∞ symmetry acts non-diagonally on massive states by mixing an infinite number of conformal families. We also present a concrete example of non-local behavior on the celestial sphere in the presence of massive scattering states.

Hyperbolic vacua in Minkowski space

Melton,

Niewinski,

Strominger

et al. 2024

Families of Lorentz, but not Poincare, invariant vacua are constructed for a massless scalar field in 4D Minkowski space. These are generalizations of the Rindler vacuum with a larger symmetry group. Explicit expressions are given as squeezed excitations of the Poincare vacuum. The effective reduced vacua on the 3D hyperbolic de Sitter slices are the well-known de Sitter α-vacua with antipodal singularities in the Wightman function. Several special interesting cases are discussed.