Soft unification of exceptional effective field theories in de Sitter space

Abstract

We uncover a surprising universal soft behaviour (USB) of a de Sitter (dS) S-matrix for \textit{all} exceptional effective field theories (EFTs) in dS space, stemming from the recently proposed generalised energy conservation (GEC) condition. At leading order in the soft limit, the dS S-matrices for all exceptional EFTs in four spacetime dimensions exhibit no scaling with the soft momentum, i.e. $\lim_{k\rightarrow 0}\mathcal{A}(k)\sim\mathcal{O}(1)$, a feature we term USB. We specifically show that USB fixes the four-point amplitudes in Dirac-Born-Infeld (DBI) theory and Special Galileon, and six-point amplitude in $SU(N)$ Non-Linear Sigma Model (NLSM) given the minimal derivative count. We then conjecture USB fixes the interactions of all exceptional EFTs to all orders, thereby providing a unification criterion for them. Our result further underpins the idea that $Δ\geq 4$ exceptional theories in dS are characterised by the spectrum and stability requirement alone, resonating with the low energy theory of gravity--General Relativity.