Constraints on a Gravitational Higgs Mechanism

Abstract

We show that it is impossible to improve the high-energy behavior of the tree-level four-point amplitude of a massive spin-2 particle by including the exchange of any number of scalars and vectors in four spacetime dimensions. This constrains possible weakly coupled ultraviolet extensions of massive gravity, ruling out gravitational analogues of the Higgs mechanism based on particles with spins less than two. Any tree-level ultraviolet extension that is Lorentz invariant and unitary must involve additional massive particles with spins greater than or equal to two, as in Kaluza-Klein theories and string theory.

arXiv comment31 pages. v2 refs added and typo fixed

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• Gauged Galileons
• Supersymmetric Massive Gravity
• Crystal gravity
• Conformal/Poincaré Coset, Cosmology, and Descendants of Lovelock Terms
• Resolving the vDVZ and Strong Coupling Problems in Massive Gravity and Bigravity
• Dynamical mass generation of spin-2 fields in de Sitter space for an $O(N)$ symmetric model at large $N$
• A unique coupling of the massive spin-2 field to supergravity