Journal Article

Unitarization from geometry

Hinterbichler, Kurt, Bonifacio, James

2019

Overview

A bstract 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.

• Publisher: Springer Berlin Heidelberg,Springer Nature B.V,Springer Berlin,SpringerOpen
• Subject: Amplitudes / Classical and Quantum Gravitation / CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS / Classical Theories of Gravity / Couplings / Effective Field Theories / Eigenvalues / Eigenvectors / Elementary Particles / Feynman diagrams / Field Theories in Higher Dimensions / Gravitons / High energy physics / Manifolds (mathematics) / Operators (mathematics) / Physics / Physics and Astronomy / Quantum Field Theories / Quantum Field Theory / Quantum Physics / Regular Article - Theoretical Physics / Relativity / Relativity Theory / Scattering Amplitudes / String Theory / Sum rules / Upper bounds