Fermionic Boundary Correlators in (EA)dS space

TL;DR

This paper develops a bootstrap approach to compute fermionic boundary correlators in (EA)dS space, deriving new cutting rules and analyzing the structure of wavefunction coefficients influenced by curvature and exchange processes.

Contribution

It introduces the first cutting rules for fermionic exchange in (EA)dS and systematically determines fermionic wavefunction coefficients using conformal Ward identities.

Findings

Derived fermionic three- and four-point wavefunction coefficients.

Established the relation between Ward identities and flat-space amplitudes.

Revealed sign differences in exchange contributions between dS and EAdS.

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 result is reminiscent of the classic analysis by Pilch, van Nieuwenhuizen, and Sohnius, though formulated in an on-shell framework.