# Where is String Theory?

### Andrea Guerrieri, Joao Penedones, Pedro Vieira

Andrea Guerrieri, Joao Penedones, Pedro Vieira

**4/2/21**Published in : arXiv:2102.02847

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 \alpha 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). A whole semi-infinite region \alpha \gtrsim 0.14 is allowed by the primal bootstrap (the garden). A finite intermediate region is excluded by non-perturbative unitarity (the swamp). Remarkably, string theory seems to cover all (or at least almost all) the garden from very large positive \alpha -- at weak coupling -- to the swamp boundary -- at strong coupling.