Effective Field Theory Islands from Perturbative and Nonperturbative Four-Graviton Amplitudes

TL;DR

This paper demonstrates that gravitational effective field theories are confined to tiny parameter regions, supported by explicit perturbative and nonperturbative four-graviton amplitude calculations across various dimensions.

Contribution

It provides the first nonperturbative example of a supersymmetric field theory coupled to gravity and generalizes perturbative models to higher dimensions, showing consistent small EFT islands.

Findings

Nonperturbative D=4, N=1 supersymmetric model on the same EFT islands as string theory models.

Perturbative models in D dimensions also confined to small EFT islands.

Explicit amplitude calculations support the tiny size of allowed EFT regions.

Abstract

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