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.

arXiv comment33 pages, 1 figure. v2 : Minor corrections and simplifications, added references. v3 : matches published version

References in corpus (76)

• Non-Gaussian features of primordial fluctuations in single field inflationary models
• The Dynamics of General Relativity
• The dS/CFT Correspondence
• Quantum Contributions to Cosmological Correlations
• Writing CFT correlation functions as AdS scattering amplitudes
• Spinning Conformal Correlators
• Conformal Vacua and Entropy in de Sitter Space
• Projectors, Shadows, and Conformal Blocks
• Partial Masslessness of Higher Spins in (A)dS
• Spinning Conformal Blocks
• TASI Lectures on Inflation
• On the eigenfunctions of the Dirac operator on spheres and real hyperbolic spaces
• Spinning AdS Propagators
• Spinors and the AdS/CFT correspondence
• Two-point Functions and Quantum Fields in de Sitter Universe
• Holography for Cosmology
• Six-dimensional Methods for Four-dimensional Conformal Field Theories
• Bootstrapping Inflationary Correlators in Mellin Space
• The Cosmological Bootstrap: Weight-Shifting Operators and Scalar Seeds
• De Sitter Musings
• A Mellin Space Approach to Cosmological Correlators
• Analyticity and Unitarity for Cosmological Correlators
• CMB from CFT
• Boundary Conformal Field Theory and a Boundary Central Charge
• Late-time Structure of the Bunch-Davies De Sitter Wavefunction
• Weight Shifting Operators and Conformal Blocks
• Bootstrapping 3D Fermions
• Holography for inflation using conformal perturbation theory
• Euclidian Vacuum Mode Functions for a Scalar Field on Open De Sitter Spacetime
• The "in-in" Formalism and Cosmological Perturbations
• From AdS to dS Exchanges: Spectral Representation, Mellin Amplitudes and Crossing
• Towards a quantum theory of de Sitter space
• Quantum de Sitter horizon entropy from quasicanonical bulk, edge, sphere and topological string partition functions
• From dS to AdS and back
• Static Patch Solipsism: Conformal Symmetry of the de Sitter Worldline
• On the Equivalence between Euclidean and In-In Formalisms in de Sitter QFT
• Cutting Cosmological Correlators
• From Locality and Unitarity to Cosmological Correlators
• Partially Massless Fields During Inflation
• Arbitrary Spin Representations in de Sitter from dS/CFT with Applications to dS Supergravity
• Spinning Witten Diagrams
• Conformal correlators of mixed-symmetry tensors
• Asymptotic Symmetries and Charges in De Sitter Space
• Mixed-symmetry fields in de Sitter space: a group theoretical glance
• TASI lectures on AdS/CFT
• De Sitter Horizons & Holographic Liquids
• Cosmological Polytopes and the Wavefunction of the Universe
• Massive Spin-2 Field in De Sitter Space
• Fermionic current and Schwinger effect in de Sitter spacetime
• Unitarity Methods in AdS/CFT
• Polarized Dirac fermions in de Sitter spacetime
• Inflationary Consistency Conditions from a Wavefunctional Perspective
• From Amplitudes to Contact Cosmological Correlators
• Partially-massless higher-spin algebras and their finite-dimensional truncations
• Group theoretical approach to quantum fields in de Sitter space I. The principal series
• Fermion Propagator in Cosmological Spaces with Constant Deceleration
• AdS Weight Shifting Operators
• Group theoretical approach to quantum fields in de Sitter space II. The complementary and discrete series
• Three-dimensional de Sitter horizon thermodynamics
• Future Boundary Conditions in De Sitter Space
• Spinor Exchange in AdS_{d+1}
• Helicity basis for three-dimensional conformal field theory
• From euclidean field theory to quantum field theory
• Holographic Representation of Local Operators In De Sitter Space
• On conformal correlators and blocks with spinors in general dimensions
• Fermions in Geodesic Witten Diagrams
• A Compendium of Sphere Path Integrals
• Spinor-helicity variables for cosmological horizons in de Sitter space
• An invitation to the principal series
• Conformally covariant quantization of Maxwell field in de Sitter space
• Higher spin de Sitter quasinormal modes
• Unitarity at the Late time Boundary of de Sitter
• Conformally related massless fields in dS, AdS and Minkowski spaces
• Integral representation of the Feynman propagators of the Dirac fermions on the de Sitter expanding universe
• A Sum Rule for Boundary Contributions to the Trace Anomaly
• Spinors in Supersymmetric dS/CFT

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