Two light rays meet at a point and then diverge. Their paths form two intersecting surfaces in spacetime — null hypersurfaces (boundaries along which light propagates). It is on such a pair of surfaces that physicists can set initial data for Einstein's equations. This is called the characteristic Cauchy problem. Until now, it had only been studied within classical physics.

The authors of the new work take a step into the quantum world. Each light surface is quantized separately, relying on symmetries at the shared boundary — a two-dimensional 'corner' where the surfaces intersect. On this corner live special transformations: supertranslations, superrotations, and superboosts. In the quantum version, supertranslations behave unusually: they do not preserve the algebra but turn into quantum channels. To incorporate them into the overall scheme, the authors apply a generalization of Stinespring's dilation theorem.

By gluing the two quantized surfaces together, physicists obtain a single algebra for the entire region. All gravitational constraints dictated by Einstein's equations are built into it. This is not a ready-made solution to all problems, but it is an important step toward understanding quantum gravity in bounded regions of spacetime.

This is how a candidate for an 'on-shell algebra' is born — a mathematical framework describing quantum states of the gravitational field in a given volume. For now, without accounting for caustics (places where light rays focus), but with a clear program for future research.