Enhanced soft limits in de Sitter space

Abstract

In flat space, the scattering amplitudes of certain scalar effective field theories exhibit enhanced soft limits due to the presence of hidden symmetries. In this paper, we show that this phenomenon extends to wavefunction coefficients in de Sitter space. Using a representation in terms of boundary conformal generators acting on contact diagrams, we find that imposing enhanced soft limits fixes the masses and four-point couplings (including curvature corrections) in agreement with Lagrangians recently derived from hidden symmetries. Higher-point couplings can then be fixed using a bootstrap procedure which we illustrate at six points. We also discuss implications for the double copy in de Sitter space.

Shift Symmetries and AdS/CFT

“…However, some of the shift fields have known fully interacting extensions that preserve the shift symmetries in a non-trivial way. For example the k = 0, 1, 2 scalars lead to AdS versions of the pion chiral Lagrangian, DBI, and special galileon, respectively [10,60,61]. Another example is the self-interacting spin 1, k = 0 theory [62,63], which was found in the massless, fixed curvature decoupling limit of various ghost-free interacting theories for a massive graviton [64] on AdS.…”

“…This naturally leads to the question of what the analogous properties of shift symmetric theories in other spacetimes are. In dS, it was recently demonstrated that, at least at the lowest few orders in powers of the fields, the momentum space boundary wavefunction coefficients of the exceptional theories satisfy soft theorems that can be used to bootstrap the theories [61] (see also [67] for the flat space version, and [68][69][70] for earlier studies of soft limits of inflationary correlators). It would be interesting to study the higher point correlators of the CFT duals to the interacting exceptional theories in AdS, and to see how the non-linear shift symmetry manifests.…”

“…In the case of the 2 point function, this constraint is fairly weak and is in fact satisfied by any correlator given by a positive power of p, which include those of non-shift symmetric scalars. The Ward identities will become more non-trivial and constraining for higher point correlators in interacting theories, as in[61].…”

Soft theorems for boosts and other time symmetries

“…Soft theorems also provide a useful organizing principle by which to classify effective field theories from the on-shell perspective. Field theories with enhanced symmetries lead to enhanced Adler zeroes of scattering amplitudes [10][11][12][13], and their corresponding wavefunction coefficients satisfy particular Ward identities [16,17].…”

“…where the ellipsis represents terms involving two or more ζs. 17 Translating into the notation of section 2, we have…”