Quantum gravity is like a theater where spacetime is the stage and fields are the actors. When the stage has an edge, you need to know exactly what happens at the boundary; otherwise, the play falls apart. In 2018, Edward Witten proposed an elegant recipe for such a case. He said: fix the shape at the boundary, like stretching a canvas, and the mean curvature, that is, how curved the stage is on average. Everything else can respond freely, like living tissue.

In the new work, this recipe was stress-tested against supersymmetry — a hypothetical symmetry that gives every particle a partner. The graviton, the carrier of gravity, gets the gravitino as its partner. The question was sharp: can you impose a boundary condition so that half of supersymmetry survives? The answer is no. As soon as you choose a natural condition for the gravitino at the boundary, it immediately responds to that very part of the curvature that Witten's recipe left free. A conflict arises: the gravitino demands control over what should be free to breathe.

The obstacle is not due to a poor choice of formulas. The authors went through all conceivable options — local, nonlocal, with various auxiliary conditions. The blockage occurs at every point of the boundary and for any momentum along it. The very structure of the equations allows no compromise: it is like trying to open and lock a door at the same time. Importantly, the ban is linear and appears at the highest derivative level: it is not global and not related to nonlinear effects. In principle, in a full nonlinear theory, one could bypass it by coupling the free curvature to the squares of the gravitino. But in the linear approximation, it is a dead end. The result delineates the boundaries within which creators of quantum gravity will have to work.