Unitarization from Geometry

Abstract

We study the perturbative unitarity of scattering amplitudes in general dimensional reductions of Yang-Mills theories and general relativity on closed internal manifolds. For the tree amplitudes of the dimensionally reduced theory to have the expected high-energy behavior of the higher-dimensional theory, the masses and cubic couplings of the Kaluza-Klein states must satisfy certain sum rules that ensure there are nontrivial cancellations between Feynman diagrams. These sum rules give constraints on the spectra and triple overlap integrals of eigenfunctions of Laplacian operators on the internal manifold and can be proven directly using Hodge and eigenfunction decompositions. One consequence of these constraints is that there is an upper bound on the ratio of consecutive eigenvalues of the scalar Laplacian on closed Ricci-flat manifolds with special holonomy. This gives a sharp bound on the allowed gaps between Kaluza-Klein excitations of the graviton that also applies to Calabi-Yau compactifications of string theory.

arXiv comment53 pages. v2 refs added. v3 fixed typos

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• Amplitudes and 4D Gauss-Bonnet Theory
• Positivity Constraints on Interacting Spin-2 Fields
• Massive Spin-2 Scattering Amplitudes in Extra-Dimensional Theories
• Positivity Constraints on Interacting Pseudo-Linear Spin-2 Fields
• Dark matter interacting via a massive spin-2 mediator in warped extra-dimensions
• Kaluza-Klein from Colour-Kinematics Duality for Massive Fields
• Scattering Amplitudes of Massive Spin-2 Kaluza-Klein States Grow Only as $\mathcal{O}(s)$
• Structure of Kaluza-Klein Graviton Scattering Amplitudes from Gravitational Equivalence Theorem and Double-Copy
• Structure of Chern-Simons Scattering Amplitudes from Topological Equivalence Theorem and Double-Copy
• Spin-2 KK Mode Scattering in Models with a Massive Radion
• Bootstrap Bounds on Closed Einstein Manifolds
• Calabi-Yau CFTs and Random Matrices
• Fakeons and microcausality: light cones, gravitational waves and the Hubble constant
• Bootstrapping Closed Hyperbolic Surfaces
• Unitarity in KK-graviton production: A case study in warped extra-dimensions
• Quantum field theories of arbitrary-spin massive multiplets and Palatini quantum gravity
• Bootstrap Bounds on Closed Hyperbolic Manifolds
• Soft Theorems from Compactification
• Gravitational Equivalence Theorem and Double-Copy for Kaluza-Klein Graviton Scattering Amplitudes
• Symmetries, Spin-2 Scattering Amplitudes, and Equivalence theorems in Warped Five-Dimensional Gravitational Theories
• Massive Color-Kinematics Duality and Double-Copy for Kaluza-Klein Scattering Amplitudes
• Gravity-Matter Sum Rules in models with a single extra-dimension
• Topological Equivalence Theorem and Double-Copy for Chern-Simons Scattering Amplitudes
• Symmetry and Unification from Soft Theorems and Unitarity
• AdS${}_3$/AdS${}_2$ degression of massless particles
• Scattering amplitudes in the Randall-Sundrum model with brane-localized curvature terms
• A unique coupling of the massive spin-2 field to supergravity