# Constraints on a Gravitational Higgs Mechanism

## TL;DR

This paper demonstrates that in four dimensions, the high-energy behavior of massive spin-2 particles cannot be improved by scalar or vector exchanges, constraining possible UV completions of massive gravity.

## Contribution

It proves that gravitational Higgs mechanisms with particles of spin less than two cannot improve high-energy behavior, requiring higher-spin particles for consistent UV extensions.

## Key findings

- Scalar and vector exchanges do not improve high-energy behavior of massive spin-2 amplitudes.
- UV extensions must include particles with spin ≥ 2, like in Kaluza-Klein or string theories.
- Constraints rule out certain gravitational Higgs mechanisms.

## 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.