Nonperturbative bounds on four-dimensional graviton scattering
In plain words
In ten and eleven dimensions, bootstrap methods have mapped which graviton-scattering amplitudes are allowed and where string theory lies. In four dimensions the same analysis is blocked by infinities from very low-energy gravitons.
Precise statement
For $D = 4$ $2\to 2$ graviton scattering with Newton constant $G$, determine nonperturbatively (without assuming a weakly coupled UV completion) the allowed range of the leading higher-derivative coefficients ($R^{3}$ and $R^{4}$ terms) in units of the cutoff, using full nonlinear unitarity. The $D = 10$ analogue was mapped by Guerrieri, Penedones, Vieira (Phys. Rev. Lett. 127, 081601, 2021); in $D = 4$ the infrared divergences must be handled first.
What would settle it
A numerical bootstrap in $D = 4$ with a controlled infrared treatment giving converged bounds.