Abstract
In this paper we investigate the decoupling limit of a particular class of multi-gravity theories, i.e. of theories of interacting spin-2 fields. We explicitly compute the interactions of helicity-0 modes in this limit, showing that they take on the form of multi-Galileons and dual forms. In the process we extend the recently discovered Galileon dualities, deriving a set of new multi-Galileon dualities. These are also intrinsically connected to healthy, but higher-derivative, multi-scalar field theories akin to `beyond Horndeski' models.
Highlights
For the model itself and [13] for investigations of its decoupling limit), we here probe the decoupling limit of (Hinterbichler-Rosen) Multi-Gravity theories [14] for the first time
These are described by Galileon interactions [24] for the helicity-0 scalar dof and the dualities relating these interactions can be understood as abstracted duality transformations [22] resulting from transformations on the coset space of GAL(d, 1)/SO(d − 1, 1) [27]
The duality can be extended to ‘generalized galileons’ [23]. The existence of these dualities is deeply linked to the non-uniqueness of the way in which gauge dof ’s can be added to the theory in order to restore full diffeomorphism invariance - a feature that is made explicit in the link field formulation for Multi-Gravity theories [28,29,30,31,32]. Using this formulation and the decoupling limit interactions for classes of Multi-Gravity models, in this paper we extend the field Galileon dualities hitherto discovered to Multi-Galileon dualities and show how they can be understood both as inherited from diffeomorphism invariance and as abstracted duality transformations
Summary
A theory of a massless spin-2 particle, propagates two dof ’s (around flat space and in the absence of a coupling to matter). We may restore full diffeomorphism invariance by performing either of the two following Stuckelberg replacements patterned after the symmetry we are restoring and at the expense of introducing extra (gauge) fields gμν → ∂μY α∂ν Y βgαβ [Y (x)] , ημν → ∂μYα∂ν Yβηαβ. An important point is that the replacement (2.3) is finite order in A and π, whereas (2.2) is not due to the dependence on gαβ [Y (x)] (a straightforward way to see this is to Taylor-expand gαβ [Y (x)] - see [1]) This makes identifying the interactions between different helicity modes very straightforward when (2.3) is used to restore diffeomorphism invariance in the action.. The potential is a Lorentzscalar built from the different g(i) and their inverses and all N fields are dynamical in contrast to the massive gravity model above, which was really a bigravity theory with one non-dynamical (fixed) field η.4. As we shall see the fact that we can choose between two such replacements and two equivalent ways of capturing the helicity-0 mode (π and φ) here is intrinsically linked to the existence of Galileon dualities
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