Generating functional for gravitational null initial data

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 is treated as an internal boundary between two adjacent slabs of spacetime. The paper concludes with a proposal for the construction of the gravitational transition amplitudes in the bulk via a gluing prescription for edge states across two-dimensional corners, thus providing a proposal for a quasi-local realisation of the holographic principle at the light front.