EFT of Interacting Spin-2 Fields

TL;DR

This paper develops effective field theories for multiple interacting massive spin-2 fields, identifying ghost issues and establishing a ghost-free class with kinetic mixing, culminating in a bi-Galileon decoupling limit.

Contribution

It introduces two classes of EFTs for interacting spin-2 fields, analyzes ghost presence, and derives a ghost-free decoupling limit with Galileon duality, advancing understanding of consistent massive gravity theories.

Findings

Ghosts appear in potential-only interactions at low scales.

Including kinetic mixing removes ghosts and maintains a high strong coupling scale.

Decoupling limit is a bi-Galileon theory, ensuring consistency.

Abstract

We consider the effective field theory of multiple interacting massive spin-2 fields. We focus on the case where the interactions are chosen so that the cutoff is the highest possible, and highlight two distinct classes of theories. In the first class, the mass eigenstates only interact through potential operators that carry no derivatives in unitary gauge at leading order. In the second class, a specific kinetic mixing between the mass eigenstates is included non-linearly. Performing a decoupling and ADM analysis, we point out the existence of a ghost present at a low scale for the first class of interactions. For the second class of interactions where kinetic mixing is included, we derive the full $\Lambda_3$ decoupling limit and confirm the absence of any ghosts. Nevertheless both formulations can be used to consistently describe an EFT of interacting massive spin-2 fields which, for a suitable technically natural tuning of the EFT, have the same strong coupling scale $\Lambda_3$. We identify the generic form of EFT corrections in each case. By using Galileon Duality transformations for the specific case of two massive spin-2 fields with suitable couplings, the decoupling limit theory is shown to be a bi-Galileon.