Positivity Constraints on Interacting Spin-2 Fields

TL;DR

This paper uses positivity bounds on scattering amplitudes to constrain the parameter space of interacting spin-2 field theories, revealing that interactions impose stricter bounds and can potentially raise the EFT cutoff.

Contribution

It demonstrates that interactions between multiple spin-2 fields lead to more stringent positivity bounds, refining the allowed EFT parameter space and suggesting relations that may increase the cutoff.

Findings

Interactions tighten bounds on EFT parameters.

Adding fields introduces more positivity bounds.

Positivity bounds favor operator relations that raise the cutoff.

Abstract

The consistency of the EFT of two interacting spin-2 fields is checked by applying forward limit positivity bounds on the scattering amplitudes to exclude the region of parameter space devoid of a standard UV completion. We focus on two classes of theories that have the highest possible EFT cutoff, namely those theories modelled on ghost-free interacting theories of a single massive spin-2 field. We find that the very existence of interactions between the spin-2 fields implies more stringent bounds on all the parameters of the EFT, even on the spin-2 self-interactions. This arises for two reasons. First, with every new field included in the low-energy EFT, comes the `knowledge' of an extra pole to be subtracted, hence strengthening the positivity bounds. Second, while adding new fields increases the number of free parameters from the new interactions, this is rapidly overcome by the increased number of positivity bounds for different possible scattering processes. We also discuss how positivity bounds appear to favour relations between operators that effectively raise the cutoff of the EFT.