EFT of interacting spin-2 fields

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

doi:10.1007/jhep01(2020)131

Lasma Alberte, Justinas Rumbutis + Show 3 more

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https://doi.org/10.1007/jhep01(2020)131

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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 Λ3-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 Λ3. 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.

Highlights

The search for all possible consistent field theories for various spins is a longstanding and ongoing research topic of fundamental importance
We identify the generic form of effective field theories (EFTs) corrections in each case
To summarize the conclusions of the analysis of this and the previous sections, the cycle theories do in general have ghosts from the perspective of an ADM analysis, but are consistent as EFTs with a cutoff scale that is at most Λ3, which can be determined from the analysis of the helicity-2/helicity-0 sector alone

Summary

Introduction

The search for all possible consistent field theories for various spins is a longstanding and ongoing research topic of fundamental importance. Renormalizable theories only exist for s ≤ 1, effective field theories (EFTs) can be constructed for higher spin values, notably for spin-2. An infinite number of spin-2 fields appears in Kaluza-Klein (KK) tower of states from dimensional reduction of higher dimensional gravity (see, e.g., [4, 6] for a review) and massive spin-2 states arise in the spectrum of string theory. An important question from the effective field theory viewpoint is to understand the consistency of the mutual interactions of the multiple massive spin-2 fields appearing in the KK tower. For instance in recent work it is noted that scattering amplitudes of the KK modes grow much slower than anticipated from the individual components [7] as a consequence of the underlying higher dimensional symmetry which explains in part how the cutoff of the KK theory is higher than that typically expected for an interacting theory of massive spin-2 states. In the condensed matter context, EFTs for spin-2 states have been used to describe a gapped collective excitation in fractional quantum Hall effect [8]

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