Dual actions for massless, partially-massless and massive gravitons in (A)dS

Abstract

We provide a unified treatment of electric-magnetic duality, at the action level and with manifest Lorentz invariance, for massive, massless as well as partially-massless gravitons propagating in maximally symmetric spacetimes of any dimension n > 3 . For massive and massless fields, we complete previous analyses that use parent-action techniques by giving dual descriptions that enable direct counting of physical degrees of freedom in the flat and massless limit. The same treatment is extended to the partiallymassless case, where the duality has been previously discussed in covariant form only at the level of the equations of motion. The nature of the dual graviton is therefore clarified for all values of the mass and of the cosmological constant.

Spin-2 Twisted Duality in (A)dS

“…One then uses (3.31) and the trace of (3.9), taking into account that, on shell, the traces of the four curvatures K a[n−2]|b , K C a[n−2]|bc , Q ab|cd and K ab|c vanish. We obtain Both together, they propagate the correct degrees of freedom for a partially massless spin-2 field in the flat limit, as was found and discussed in section 4.3 of [7]. The flat limit of (3.36) gives…”

“…The equations of motion for the dual gauge fields C a[n−3]|b and T a[n−2]|b derived from the Lagrangian L 0 (C, T ) -obtained by substituting (2.18) in (2.9) and given in Eq. (23) of [7] -can be written in terms of the traces of the gauge-invariant curvatures K C a[n−2]|b [2] and K T a[n−1]|b [2] . Explicitly, one has 28) and the gauge invariant tensors X and V can be expressed as…”

“…Recently [7], manifestly covariant action principles in the Stueckelberg formulation were given for dual massless, partially massless and massive spin-2 fields in maximally symmetric spacetimes of arbitrary dimensions n > 3 , such that the degrees of freedom are preserved in the flat limit. The action principles for the dual fields were also related to the standard ones for such field theories by building on the previous works [8][9][10][11][12][13][14][15][16][17][18][19].…”

“…In this Letter we focus on the massless and partially-massless cases and formulate the field equations derived from the actions of [7] as twisted-duality relations. In the massless case, our twisted-duality relation -see Eq.…”

A theory for multiple partially massless spin-2 fields

“…Actually, PM fields can be defined around D-dimensional Anti-de Sitter (AdS D ) spacetime where they are classically non-unitary. This can be seen explicitly by writing the action, which is real for both signs of the cosmological constant, in the Stueckelberg formulation[11].…”