On the (A)dS Decoupling Limits of Massive Gravity

TL;DR

This paper explores decoupling limits of ghost-free massive gravity on (A)dS spaces, revealing new interacting theories with unique symmetries and potential dualities, and analyzing their strong coupling scales and operator content.

Contribution

It introduces novel decoupling limits on (A)dS, including a Proca theory on AdS and a partially massless limit on dS, with explicit interactions and symmetry properties.

Findings

Proca theory on AdS with a specific strong coupling scale.

Finite operator set in generic partially massless limit on dS.

Infinite interactions preserving symmetries in the special partially massless case.

Abstract

We consider various decoupling limits of ghost-free massive gravity on (A)dS. The first is a decoupling limit on AdS space where the mass goes to zero while the AdS radius is held fixed. This results in an interacting massive Proca vector theory with a $\Lambda_2\sim (M_{\rm Pl} m)^{1/2}$ strong coupling scale which is ghost-free by construction and yet can not be put in the form of the generalized Proca theories considered so far. We comment on the existence of a potential duality between this Proca theory and a CFT on the boundary. The second decoupling limit we consider is a new limit on dS, obtained by sending the mass towards the finite partially massless value. We do this by introducing the scalar St\"uckelberg field which restores the partially massless symmetry. For generic values of the parameters, only a finite number of operators enter the partially massless decoupling limit and take the form of dS Galileons. If the interactions are chosen to be precisely those of the `candidate' non-linear partially massless theory, the resulting strong coupling scale has a higher value and the resulting decoupling limit includes an infinite number of interactions which we give in closed form. These interactions preserve both the linear partially massless symmetry and the dS version of the Galileon shift symmetry.