Positivity of Amplitudes, Weak Gravity Conjecture, and Modified Gravity

Area of Science:

• Theoretical physics
• Quantum gravity
• String theory

Background:

• The weak gravity conjecture (WGC) is a proposed constraint on the strength of gravity relative to other forces.
• Understanding black hole properties and their stability is crucial in quantum gravity.

Purpose of the Study:

• To derive new positivity bounds for scattering amplitudes in theories with a massless graviton.
• To provide an S-matrix proof of the weak gravity conjecture.
• To explore applications in modified gravity and effective field theories.

Main Methods:

• Derivation of new positivity bounds for scattering amplitudes.
• Analysis of implications for extremal black hole properties (M/|Q|<1).
• Application of bounds to effective field theories.

Main Results:

• New positivity bounds derived for theories with a massless graviton.
• Extremal black holes shown to be self-repulsive (M/|Q|<1).
• Extremal black holes proven unstable to decay, supporting the weak gravity conjecture.

Conclusions:

• The derived bounds offer an S-matrix proof of the weak gravity conjecture.
• The results have significant implications for black hole physics and modified gravity theories.
• Applications extend to effective field theories of Galileons, axions, and P(X) theories.