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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.
Highlights
The Higgs mechanism is a central feature of the standard model, the theory of superconductivity, and countless other more speculative scenarios
The mechanism is often conceptualized in terms of spontaneous symmetry breaking: a gauge symmetry is broken by the vacuum expectation value of some scalar Higgs field, and the massless gauge fields “eat” some components of the Higgs field to become massive, leaving behind physical scalars
Looking only at the S-matrix, we may think about the Higgs mechanism differently: it is a method of raising the ultraviolet (UV) strong coupling scale of an effective theory of self-interacting massive spin-1 particles by adding weakly coupled scalars to the theory
Summary
The Higgs mechanism is a central feature of the standard model, the theory of superconductivity, and countless other more speculative scenarios. The goal of this paper is to determine in complete generality whether it is possible to introduce additional particles with spins less than two into the effective field theory of a single massive spin-2 particle so as to improve the high-energy behavior of the tree amplitudes and raise the strong coupling scale of the low-energy theory. Our conclusions imply that for massive gravity and bigravity, any tree-level UV extension must contain additional massive particles with spins greater than or equal to two This conclusion is consistent with the arguments concerning full weakly coupled UV completions, but is a stronger statement as it concerns a UV extension and as we need no assumptions about the asymptotic behavior of the full S-matrix. Conventions on kinematics and polarizations are detailed in the Appendix A
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