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EFT of Interacting Spin-2 Fields

Lasma Alberte, Claudia de Rham, Arshia Momeni, Justinas Rumbutis, Andrew J. Tolley

TL;DR

The paper analyzes the effective field theory of multiple interacting massive spin-2 fields, focusing on two topologies—Cycle, with potential-only interactions in the mass basis, and Line, with nonlinear kinetic mixing. Through decoupling-limit and ADM analyses, it shows Cycle theories generically host Boulware-Deser ghosts at a low scale unless mixed interactions are tuned to raise the cutoff to Λ3, while Line theories achieve a Λ3 EFT without ghosts. The work clarifies the structure of leading interactions, identifies higher-derivative EFT corrections, and reveals a bi-Galileon formulation for two-field Line theories via Galileon dualities. It then extends the framework to multiple spin-2 fields and discusses implications for EFT corrections and potential UV completions, highlighting distinct phenomenological and theoretical consequences of Cycle versus Line topologies.

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 $Λ_3$ 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 $Λ_3$. 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.

EFT of Interacting Spin-2 Fields

TL;DR

The paper analyzes the effective field theory of multiple interacting massive spin-2 fields, focusing on two topologies—Cycle, with potential-only interactions in the mass basis, and Line, with nonlinear kinetic mixing. Through decoupling-limit and ADM analyses, it shows Cycle theories generically host Boulware-Deser ghosts at a low scale unless mixed interactions are tuned to raise the cutoff to Λ3, while Line theories achieve a Λ3 EFT without ghosts. The work clarifies the structure of leading interactions, identifies higher-derivative EFT corrections, and reveals a bi-Galileon formulation for two-field Line theories via Galileon dualities. It then extends the framework to multiple spin-2 fields and discusses implications for EFT corrections and potential UV completions, highlighting distinct phenomenological and theoretical consequences of Cycle versus Line topologies.

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 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 . 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.

Paper Structure

This paper contains 38 sections, 200 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The EFT of Interacting Massive Spin-2 Fields
  3. Cycle vs. Line of Interactions
  4. Cycle of Interactions - Mass eigenstates:
  5. Line of Interactions - Mass Mixings:
  6. Diffeomorphisms versus Spin-2 Gauge Invariance:
  7. Spin-2 fields as Perturbations of Metric-like Objects:
  8. Vierbein Formalism for Two Fields
  9. Cycle of Interactions
  10. Line of Interactions
  11. Symmetric Vierbeins:
  12. ADM Constraint Analysis
  13. Decoupling Limit for the Cycle of Interactions
  14. Helicity-two/Helicity-zero Sector
  15. Helicity-one/Helicity-zero Sector
  16. ...and 23 more sections

Figures (1)

  • Figure 1: Different interacting topologies Hinterbichler:2012cn. For free fields both models are equivalent (after diagonalization), but the models differ nonlinearly. In terms of the mass eigenstates, the cycle of interactions [left] only includes potential interactions, while the line of interactions [right] also includes a specific class of kinetic mixing.