Conformal Wavefunctions for Graviton Amplitudes

TL;DR

This paper explores the conformal properties of graviton wavefunctions in asymptotically flat spacetime, constructing a holographic mapping between conformal representations and gravitational perturbations.

Contribution

It introduces a method to analyze graviton representations using conformal wavefunctions and establishes a holographic correspondence with flat spacetime perturbations.

Findings

Decomposition of Weyl scalars into principal series representations

Construction of an invertible holographic map

Analysis of conformal transformations on the celestial sphere

Abstract

The extended-BMS algebra of asymptotically flat spacetime contains an SO(3,1) subgroup that acts by conformal transformations on the celestial sphere. It is of interest to study the representations of this subgroup associated with gravitons. To reduce the equation of motion to a Schrodinger-like equation it is necessary to impose a non-covariant gauge condition. Using these solutions, leading-order gauge invariant Weyl scalars are then computed and decomposed into families of unitary principal series representations. An invertible holographic mapping is constructed between these unitary principal series operators and massless spin-2 perturbations of flat spacetime.