Effective field theories and cosmological scattering equations

Abstract

We propose worldsheet formulae for wavefunction coefficients of the massive non-linear sigma model (NLSM), scalar Dirac-Born-Infeld (DBI), and special Galileon (sGal) theories in de Sitter momentum space in terms of the recently proposed cosmological scattering equations constructed from conformal generators in the future boundary. The four-point integrands are assembled from simple building blocks and we identify a double copy prescription mapping the NLSM wavefunction coefficient to the DBI and sGal wavefunction coefficients, including mass deformations and curvature corrections. Finally, we compute the soft limits of these wavefunction coefficients and find that they can be written in terms of boundary conformal generators acting on contact diagrams.

Enhanced soft limits in de Sitter space

“…and used to explore the double copy for effective scalar theories in [50] (the double copy for effective scalar theories in AdS was also explored from various other points of view in [53,67,68]). In more detail, a generalised double copy for 4-point wavefunction coefficients was proposed in terms of unfixed parameters encoding masses and curvature corrections.…”

“…We will focus on effective scalar theories with mass m 2 = ∆(d − ∆). The discussion will be very schematic but the interested reader can find more details in [50]. A tree-level n-point wavefunction coefficient can be written as an integral over n-punctures on the sphere:…”

“…To study soft limits of wavefunction coefficients, it is natural to work in dS momentum space [28][29][30], which is also the standard language used for cosmology (see [24,[31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46] for some recent developments). Another technique we will employ is to express the wavefunction coefficients in terms of boundary conformal generators acting on contact diagrams [47][48][49][50][51][52][53][54]. Soft limits can then computed by Taylor expanding bulk-to-boundary propagators in the contact diagram, acting on them with boundary conformal generators, and using the equations of motion to remove terms which are not linearly independent.…”

“…For the NLSM, we find that enhanced soft limits forbid mass terms or curvature corrections, so the Lagrangian can be trivially lifted from flat space. These results in turn allow us to fix all the parameters of the generalised double copy prescription proposed in [50], which relates the 4-point treelevel wavefunction coefficient of the NLSM model to those of the DBI and sGal theories. 1 Above four points, there must be non-trivial cancellations between contact and exchange Witten diagrams in order to have enhanced soft limits.…”

Flavour-kinematics duality for Goldstone modes

“…Finally, it would be interesting to investigate whether the double copy that has been identified for on-shell amplitudes also extends to off-shell aspects such as correlators and wavefunctionals. This issue was addressed very recently [28], where it was found that the most straightforward implementation of the double copy structure does not work (however, see also the analysis of [72] employing cosmological scattering equations). Given the offshell mapping outlined in section 2, it would be interesting to see whether this could be adapted for the gravity-coupled SO(M, N ) NL σ-model, and whether this would allow for a mapping onto multi-DBI and SG.…”