We construct the Wightman function for symmetric traceless tensors and Dirac fermions in dSd+1 in a coordinate and index free formalism using a d + 2 dimensional ambient space. We expand the embedding space formalism to cover spinor and tensor fields in any even or odd dimension. Our goal is to furnish a self-contained toolkit for the study of fields of arbitrary spin in de Sitter, with applications to cosmological perturbation theory. The construction for spinors is shown in extensive detail. Concise expressions for the action of isometry generators on generic bulk fields, the 2-point function of bulk spinors, and a derivation of the uplift of the spinorial covariant derivative are included.

In the context of boundary conformal field theory, we derive a sum rule that relates two and three point functions of the displacement operator. For four dimensional conformal field theory with a three dimensional boundary, this sum rule in turn relates the two boundary contributions to the anomaly in the trace of the stress tensor. We check our sum rule for a variety of free theories and also for a weakly interacting theory, where a free scalar in the bulk couples marginally to a generalized free field on the boundary.

We use the equations of motion in combination with crossing symmetry to constrain the properties of interacting fermionic boundary conformal field theories. This combination is an efficient way of determining operator product expansion coefficients and anomalous dimensions at the first few orders of the ϵ expansion. Two necessary ingredients for this procedure are knowledge of the boundary and bulk spinor conformal blocks. The bulk spinor conformal blocks are derived here for the first time. We then consider a number of examples. For ϕ a scalar field and ψ a fermionic field, we study the effects of a $$ \phi \overline{\psi}\psi $$ ϕ ψ ¯ ψ coupling in 4 – ϵ dimensions, a $$ {\phi}^2\overline{\psi}\psi $$ ϕ 2 ψ ¯ ψ coupling in 3 – ϵ dimensions, and a $$ {\left(\overline{\psi}\psi \right)}^2 $$ ψ ¯ ψ 2 coupling in 2 + ϵ dimensions. We are able to compute some new anomalous dimensions for operators in these theories. Finally, we relate the anomalous dimension of a surface operator to the behavior of the charge density near the surface.

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