Effective Field Theory islands from perturbative and nonperturbative four-graviton amplitudes

Theoretical data obtained from physically sensible field and string theory models suggest that gravitational Effective Field Theories (EFTs) live on islands are tiny compared to current general bounds determined unitarity, causality, crossing symmetry, a good high-energy behavior. In this work, we present explicit perturbative nonperturbative $2 \to 2$ graviton scattering amplitudes their associated low-energy expansion in spacetime dimensions $D\geq 4$ support notion. Our new results include first example consisting of $D=4$, $\mathcal{N}=1$ supersymmetric is coupled weakly gravity. We show model lies the same identified using four-dimensional based minimally-coupled matter circulating loop. Furthermore, generalize previous massive spin-0 spin-1 states loop $D$ dimensions. Remarkably, again find EFT coefficients lie small islands. These offer useful guide towards constraining possible extensions Einstein