Finite energy sum rules for gravitational Regge amplitudes

Abstract

We develop a framework to derive consistency constraints on gravitational Regge amplitudes based on the finite energy sum rules (FESRs), which directly connect gravitational Regge amplitudes at a finite ultraviolet scale with infrared physics without suffering from super-Planckian physics. For illustration, we consider four-point scattering of an identical massless scalar coupled to gravity. First, we derive multiple FESRs without relying on the $s\text{-}t\text{-}u$ permutation invariance. We then make use of FESRs, crossing symmetry, and other principles such as unitarity, to derive bounds on the Regge parameters. The bounds result in infrared finite gravitational positivity bounds in four spacetime dimensions.

24 pages plus appendices, 11 figures, v2: bounds in higher spacetime dimensions added, matches the version to appear in JHEP

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Cited by in corpus (6)

• Massive Gravity is not Positive
• Non-Forward UV/IR Relations
• Black Hole Extremality in Nonlinear Electrodynamics: A Lesson for Weak Gravity and Festina Lente Bounds
• Gravitational Positivity for Phenomenologists: Dark Gauge Boson in the Swampland
• Lectures in Quantum Gravity
• Spectral Constraints on Theories of Colored Particles and Gravity