Tensors and Spinors in de Sitter Space

Abstract

We construct the Wightman function for symmetric traceless tensors and Dirac fermions in dS${}_{d+1}$ 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.

33 pages, 1 figure. v2 : Minor corrections and simplifications, added references. v3 : matches published version

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• Boundary Conformal Field Theory and a Boundary Central Charge
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Cited by in corpus (14)

• The Källén-Lehmann representation in de Sitter spacetime
• The graviton four-point function in de Sitter space
• Fermions in Boundary Conformal Field Theory : Crossing Symmetry and $\epsilon$-Expansion
• de Sitter at all loops: the story of the Schwinger model
• The de Sitter group and its presence at the late-time boundary
• (Non-)unitarity of strictly and partially massless fermions on de Sitter space II: an explanation based on the group-theoretic properties of the spin-3/2 and spin-5/2 eigenmodes
• Pole-skipping in two-dimensional de Sitter spacetime and double-scaled SYK model
• New conformal-like symmetry of strictly massless fermions in four-dimensional de Sitter space
• Partition functions and entanglement entropy: Weyl graviton and conformal higher spin fields
• Fermionic Shift Symmetries in (Anti) de Sitter Space
• RG flows in de Sitter: c-functions and sum rules
• Spinors and conformal correlators
• Laplacian and codifferential operators on p-forms in (Anti)-de Sitter spaces: restriction and continuation
• FLRW embeddings in ${\mathbb{R}}^{n+2}$, differential geometry and conformal photon propagator