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New Exceptional EFTs in de Sitter Space from Generalised Energy Conservation

Zong-Zhe Du, David Stefanyszyn

TL;DR

This work investigates scattering in de Sitter space by constructing a de Sitter S-matrix from glued Poincaré patches and enforcing generalised energy conservation (GEC) through the vanishing of the residue at $η=0$ under BD vacua. By applying GEC to four-point amplitudes of exceptional-series scalars, the authors recover the Dirac-Born-Infeld (DBI) theory at $Δ=4$ and the Special Galileon at $Δ=5$, and provide evidence for new exceptional EFTs at higher conformal dimensions with quartic self-interactions uniquely fixed by a single coupling. They present explicit Lagrangians up to $Δ=7$ showing a pattern of fixed quartic couplings and conjecture that an infinite tower of such theories exists for all integer $Δ≥4$, with Δ≥6 potentially requiring additional degrees of freedom. The results offer a stability-driven, on-shell pathway to identify fundamental EFTs in de Sitter space and hint at deeper connections to de Sitter algebras and higher-spin structures, motivating further exploration of the symmetry principles governing these exceptional theories.

Abstract

We discover a surprising relationship between exceptional effective field theories (EFTs) in de Sitter space and a notion of \textit{generalised energy conservation} (GEC) of an S-matrix defined in an extended Poincaré patch of four-dimensional de Sitter. By demanding that such an S-matrix only has support when the total energies of in and out states are equal, we constrain the coupling constants in theories of self-interacting scalars living in the exceptional series of de Sitter representations. We rediscover the theories of Dirac-Born-Infeld (DBI) and Special Galileon, and when increasing the conformal dimension we find evidence for new exceptional theories where the four-point scalar self interactions are uniquely fixed in terms of a single coupling constant. We conjecture that for each integer conformal dimension $Δ\geq 4$, there is at least one exceptional EFT that can be entirely fixed by GEC.

New Exceptional EFTs in de Sitter Space from Generalised Energy Conservation

TL;DR

This work investigates scattering in de Sitter space by constructing a de Sitter S-matrix from glued Poincaré patches and enforcing generalised energy conservation (GEC) through the vanishing of the residue at under BD vacua. By applying GEC to four-point amplitudes of exceptional-series scalars, the authors recover the Dirac-Born-Infeld (DBI) theory at and the Special Galileon at , and provide evidence for new exceptional EFTs at higher conformal dimensions with quartic self-interactions uniquely fixed by a single coupling. They present explicit Lagrangians up to showing a pattern of fixed quartic couplings and conjecture that an infinite tower of such theories exists for all integer , with Δ≥6 potentially requiring additional degrees of freedom. The results offer a stability-driven, on-shell pathway to identify fundamental EFTs in de Sitter space and hint at deeper connections to de Sitter algebras and higher-spin structures, motivating further exploration of the symmetry principles governing these exceptional theories.

Abstract

We discover a surprising relationship between exceptional effective field theories (EFTs) in de Sitter space and a notion of \textit{generalised energy conservation} (GEC) of an S-matrix defined in an extended Poincaré patch of four-dimensional de Sitter. By demanding that such an S-matrix only has support when the total energies of in and out states are equal, we constrain the coupling constants in theories of self-interacting scalars living in the exceptional series of de Sitter representations. We rediscover the theories of Dirac-Born-Infeld (DBI) and Special Galileon, and when increasing the conformal dimension we find evidence for new exceptional theories where the four-point scalar self interactions are uniquely fixed in terms of a single coupling constant. We conjecture that for each integer conformal dimension , there is at least one exceptional EFT that can be entirely fixed by GEC.

Paper Structure

This paper contains 16 sections, 52 equations, 2 figures.

Table of Contents

  1. Introduction and Summary
  2. Notation
  3. Exceptional EFTs from generalised energy conservation
  4. $\bullet$ $\Delta = 3$
  5. $\bullet$ $\Delta = 4$
  6. $\bullet$ $\Delta = 5$
  7. $\bullet$ $\Delta = 6$
  8. $\bullet$ $\Delta = 7$
  9. Discussion
  10. Data access statement
  11. A de Sitter S-matrix and field basis independence
  12. $\bullet$ $\Delta = 3$
  13. $\bullet$ $\Delta = 4$
  14. Application to other dimensions
  15. $\bullet$ $D = 2$
  16. ...and 1 more sections

Figures (2)

  • Figure 1: The time integration contour for a dS scattering amplitude in an eternal energy-creating universe. The contour is chosen such that the integral on the large arc vanishes for $k_T\neq 0$ while the scattering amplitude is non-vanishing only when $k_T = k_{\text{in}} - k_{\text{out}}\leq 0$.
  • Figure 2: The time integration contour for a dS scattering amplitude in an eternal energy-annihilating universe. The contour is chosen such that the integral on the large arc vanishes for $k_T\neq 0$ while the scattering amplitude is non-vanishing only when $k_T = k_{\text{in}} - k_{\text{out}}\geq 0$.

Theorems & Definitions (2)

  • Conjecture 1
  • Conjecture 2