Towards a holographic approach for gravity in asymptotically flat spacetimes

Progress in quantum gravity over the past decades has been to a large extent triggered by the holographic principle, the proposal that bulk regions of spacetime in quantum gravity are dual to non-gravitational, quantum theories living on the boundary.

While a precise realization in AdS string theory was found by Maldacena, the universal scaling law of black hole entropy with area suggests that similar dualities should exist more generally, for example in our own universe which is flat to a good degree of approximation. Nevertheless, an understanding of the nature of the holographic duality in flat space is still missing.

The goal of this proposal is to study aspects of a recently proposed two-dimensional holographic formulation of four-dimensional asymptotically flat quantum gravity, broadly defined as any theory that reduces to general relativity at long distances.

In this framework, the fundamental observables live on a two-dimensional sphere at infinity and are in one-to-one correspondence with bulk scattering amplitudes.

These new observables known as celestial amplitudes compute scattering in a basis of asymptotic boost as opposed to the usual energy momentum eigenstates and obey a wide range of constraints. During this fellowship I will investigate two main aspects of flat space holography.

On the one hand, I will study the celestial imprints of black hole scattering by computing celestial amplitudes with massive particles and analyzing their symmetry properties.

On the other hand I will exploit the flat space limit of AdS holography and apply conformal bootstrap techniques to derive new constraints on the observables of four-dimensional asymptotically flat gravity.

These results will provide insights into non-perturbative aspects of gravity in asymptotically flat spacetimes and will establish new connections among different fields and communities including asymptotic symmetries, scattering amplitudes and holography.