Where is M-theory in the space of scattering amplitudes?

Abstract

We use the S-matrix bootstrap to carve out the space of unitary, analytic, crossing symmetric and supersymmetric graviton scattering amplitudes in nine, ten and eleven dimensions. We extend and improve the numerical methods of our previous work in ten dimensions. A key new tool employed here is unitarity in the celestial sphere. In all dimensions, we find that the minimal allowed value of the Wilson coefficient $\alpha$, controlling the leading correction to maximal supergravity, is very close but not equal to the minimal value realized in Superstring theory or M-theory. This small difference may be related to inelastic effects that are not well described by our numerical extremal amplitudes. Although $\alpha$ has a unique value in M-theory, we found no evidence of an upper bound on $\alpha$ in 11D.

17 pages, 18 figures

References in corpus (4)

• Where is String Theory?
• On Unitarity of Tree-Level String Amplitudes
• $D^6{R}^4$ amplitudes in various dimensions
• Positivity of the Veneziano Amplitude in $D=4$

Cited by in corpus (8)

• Massive Gravity is not Positive
• Species scale, worldsheet CFTs and emergent geometry
• Asymptotic safety, quantum gravity, and the swampland: a conceptual assessment
• Lectures in Quantum Gravity
• A Celestial Route to AdS Bulk Locality
• On the number of Regge trajectories for dual amplitudes
• Saturating unitarity bounds at U-duality symmetric points
• Higher-Spin and Higher-Point Constraints on Stringy Amplitudes