# Generating functional for gravitational null initial data

## TL;DR

This paper introduces a boundary field theory for gravitational null initial data using dressed Chern-Simons terms and proposes a holographic approach to compute bulk transition amplitudes via boundary edge states.

## Contribution

It develops a novel boundary action involving self-dual Ashtekar variables and junction conditions, offering a new framework for gravitational transition amplitudes on null hypersurfaces.

## Key findings

- Boundary action with dressed Chern-Simons terms formulated
- Proposal for holographic construction of gravitational amplitudes
- Doubling of field content for null hypersurface interface

## Abstract

A field theory on a three-dimensional manifold is introduced, whose field equations are the constraint equations for general relativity on a three-dimensional null hypersurface. The underlying boundary action consists of two copies of the dressed Chern-Simons term for self-dual Ashtekar variables, a kinetic term for the null flag at the boundary plus additional junction conditions for the spin coefficients across the interface. In fact, there is a doubling of the field content, because the null hypersurface will be considered as an internal boundary between two adjacent slabs of spacetime. The paper concludes with a proposal for a construction of the gravitational transition amplitudes in the bulk via the auxiliary boundary field theory alone, namely by gluing amplitudes for edge states across two-dimensional corners, thus providing a proposal for a quasi-local realisation of the holographic principle at the light front.