Where Is String Theory in the Space of Scattering Amplitudes?

We use the S-matrix bootstrap to carve out the space of unitary, crossing symmetric and supersymmetric graviton scattering amplitudes in ten dimensions. We focus on the leading Wilson coefficient a controlling the leading correction to maximal supergravity. The negative region alpha < 0 is excluded by a simple dual argument based on linearized unitarity (the desert). Awhole semi-infinite region alpha greater than or similar to 0.14 is allowed by the primal bootstrap (the garden). A finite intermediate region is excluded by nonperturbative unitarity (the swamp). Remarkably, string theory seems to cover all (or at least almost all) the garden from very large positive a-at weak coupling-to the swamp boundary-at strong coupling.

Automated summary

The study employs S-matrix bootstrap to investigate graviton scattering amplitudes in ten dimensions, leading to the exclusion of a negative region, approval of a garden region, and the exclusion of an intermediate swamp region. Interestingly, string theory appears to cover almost all the garden region at weak coupling and the swamp boundary at strong coupling.