Where Is String Theory in the Space of Scattering Amplitudes?

Area of Science:

• Theoretical Physics
• High-Energy Physics
• String Theory

Background:

• Understanding quantum gravity requires analyzing scattering amplitudes.
• Maximal supergravity in ten dimensions provides a crucial theoretical framework.
• The S-matrix bootstrap offers a powerful method for constraining theoretical models.

Purpose of the Study:

• To determine the allowed parameter space for unitary, crossing symmetric, and supersymmetric graviton scattering amplitudes in ten dimensions.
• To investigate the role of the leading Wilson coefficient (α) in maximal supergravity corrections.
• To map the regions excluded or allowed by different unitarity conditions.

Main Methods:

• Utilizing the S-matrix bootstrap technique.
• Applying linearized unitarity to exclude the negative region of α.
• Employing the primal bootstrap to identify the allowed positive region of α (the garden).
• Using nonperturbative unitarity to exclude an intermediate region (the swamp).

Main Results:

• The region α<0 is excluded by linearized unitarity.
• A semi-infinite region α≳0.14 is allowed by the primal bootstrap.
• A finite intermediate region is excluded by nonperturbative unitarity.
• String theory appears to cover a significant portion of the allowed parameter space (the garden).

Conclusions:

• The S-matrix bootstrap successfully carves out the space of allowed graviton scattering amplitudes.
• String theory's predictions align well with the boundaries defined by unitarity conditions.
• The study highlights the interplay between theoretical constraints and string theory in quantum gravity.