EFT of interacting spin-2 fields

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 3decoupling 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.

Positivity constraints on interacting spin-2 fields

“…where a 1 and κ (h) 3,4 are dimensionless coupling constants. The choice of scales for the coefficients in this leading effective action will be defined in analogy to the general case [26,31] by identifying a spin-2 interaction scale M 1 and organizing the pseudo-linear theory as an EFT with the strong coupling scale Λ 3 = (m 2 1 M 1 ) 1/3 . In addition, as in [26,31] we have include an overall weak coupling parameter g * which conveniently suppresses loops if g * 1 allowing us to apply tree level positivity bounds only.…”

“…However, higher order terms do arise suppressed by the scale Λ 3 . The Λ 3 -EFT was discussed for instance in [25,31] and the higher order operators take the form…”

Positivity constraints on interacting pseudo-linear spin-2 fields

“…In a recent work [36] we applied the positivity bounds to EFTs of interacting multiple spin-2 fields described in [41], which were extensions of ghost-free massive gravity. In this paper we apply these bounds to effective field theories of one or more interacting pseudolinear massive spin-2 fields.…”

“…in the massive gravity context. In what follows, we shall not be concerned with the theory defined uniquely by the ghost-free interactions, but rather by the effective field theory with the highest cutoff, similarly to the logic followed in [36,41]. From this perspective the interactions (2.3) are to be regarded as the leading interactions in a Wilsonian effective action which contains an infinite number of terms.…”

“…are dimensionless coupling constants. The choice of scales for the coefficients in this leading effective action will be defined in analogy to the general case [36,41] by identifying a spin-2 interaction scale M 1 and organizing the pseudo-linear theory as an EFT with the strong coupling scale Λ 3 = (m 2 1 M 1 ) 1/3 . In addition, as in [36,41] we have include an overall weak coupling parameter g * which conveniently suppresses loops if g * 1 allowing us to apply tree level positivity bounds only.…”