Fermionic Boundary Correlators in (EA)dS space

TL;DR

This work extends the fermionic wavefunction coefficient bootstrap to de Sitter and Euclidean AdS spaces by enforcing conformal Ward identities and universal cutting rules. Beginning from the leading total-energy pole, the authors show that the flat-space amplitude governs the leading residue, while curvature induces subleading corrections, and they determine the full set of fermionic 3- and 4-point WFCs, including spin-1/2 and spin-3/2 sectors. The analysis provides explicit spinor-helicity decompositions, WT/CWI consistency checks, and a detailed enforcement of partial-energy poles via cutting rules, reproducing known flat-space structures in the appropriate limit. A key finding is a tension in de Sitter with conserved spin-3/2 currents: the reality conditions and dS isometries imply sign differences between graviton and photon exchange channels that spoil unitarity in the 4-fermion amplitude, pointing toward the need for higher-spin completions or alternative pole structures. Overall, the paper demonstrates that CWIs and cutting rules can uniquely constrain fermionic WFCs in (EA)dS and clarifies the role of reality conditions and WT identities in the fermionic sector, with implications for supersymmetric extensions and higher-spin theories in cosmological backgrounds.

Abstract

In this paper we bootstrap de Sitter wavefunction coefficients (WFCs) involving fermionic operators. Starting with a fixed total-energy pole order, we systematically impose the conformal Ward identities (CWI) together with cutting-rule constraints. We derive the relevant cutting rules for fermionic exchange for the first time, enabling a complete determination of fermionic three- and four-point WFCs. We show that CWI fixes the leading total-energy-pole residue to the flat-space amplitude and subleading residues to curvature induced corrections to bulk vertices. The structure of the Ward-Takahashi identities are similarly fully determined. As an application, we derive four massless spin-1/2 WFC due to graviton exchange. We also revisit the tension between conserved spin-3/2 operators and de Sitter geometry. We demonstrate that the reality conditions appropriate to dS and Euclidean AdS (EAdS) lead to distinct three-point WFCs for two spin-3/2 operators and the stress tensor. Consequently, the residue of the leading total-energy pole for the four-point WFC receives graviton- and photon-exchange contributions with opposite signs in dS, whereas they appear with the same sign in EAdS. This reproduces the classic result of Pilch, van Nieuwenhuizen, and Sohnius in an explicitly on-shell form.