The Källén-Lehmann representation in de Sitter spacetime

Abstract

We study two-point functions of symmetric traceless local operators in the bulk of de Sitter spacetime. We derive the Källén-Lehmann spectral decomposition for any spin and show that unitarity implies its spectral densities are nonnegative. In addition, we recover the Källén-Lehmann decomposition in Minkowski space by taking the flat space limit. Using harmonic analysis and the Wick rotation to Euclidean Anti de Sitter, we derive an inversion formula to compute the spectral densities. Using the inversion formula, we relate the analytic structure of the spectral densities to the late-time boundary operator content. We apply our technical tools to study two-point functions of composite operators in free and weakly coupled theories. In the weakly coupled case, we show how the Källén-Lehmann decomposition is useful to find the anomalous dimensions of the late-time boundary operators. We also derive the Källén-Lehmann representation of two-point functions of spinning primary operators of a Conformal Field Theory on de Sitter.

arXiv comment63 pages + appendices, 10 figures

References in corpus (52)

• Non-Gaussian features of primordial fluctuations in single field inflationary models
• Quantum Contributions to Cosmological Correlations
• Holography from Conformal Field Theory
• Writing CFT correlation functions as AdS scattering amplitudes
• Spinning Conformal Correlators
• Projectors, Shadows, and Conformal Blocks
• Conformal Regge theory
• Partial Masslessness of Higher Spins in (A)dS
• Gauge Invariances and Phases of Massive Higher Spins in (A)dS
• Spinning AdS Propagators
• Two-point Functions and Quantum Fields in de Sitter Universe
• Effective Conformal Theory and the Flat-Space Limit of AdS
• The IR stability of de Sitter: Loop corrections to scalar propagators
• Bootstrapping Inflationary Correlators in Mellin Space
• Analyticity and the Holographic S-Matrix
• Stability of Massive Cosmological Gravitons
• A Mellin Space Approach to Cosmological Correlators
• Infrared Sensitivity of Unstable Vacua
• The Cosmological Optical Theorem
• Analyticity and Unitarity for Cosmological Correlators
• Late-time Structure of the Bunch-Davies De Sitter Wavefunction
• Cosmological Cutting Rules
• Interacting Quantum Field Theory in de Sitter Vacua
• Static Patch Solipsism: Conformal Symmetry of the de Sitter Worldline
• Quantum de Sitter horizon entropy from quasicanonical bulk, edge, sphere and topological string partition functions
• Building a Boostless Bootstrap for the Bispectrum
• Cutting Cosmological Correlators
• Analyticity properties and thermal effects for general quantum field theory on de Sitter space-time
• A Study of Quantum Field Theories in AdS at Finite Coupling
• Harmonic Analysis and Mean Field Theory
• de Sitter Vacua, Renormalization and Locality
• Signals of a Quantum Universe
• Mixed-symmetry fields in de Sitter space: a group theoretical glance
• Squeezed States in the de Sitter Vacuum
• Massless interacting quantum fields in deSitter spacetime
• State/Operator Correspondence in Higher-Spin dS/CFT
• Spinning AdS Loop Diagrams: Two Point Functions
• Triangular invariants, three-point functions and particle stability on the de Sitter universe
• Shift Symmetries in (Anti) de Sitter Space
• Infrared dynamics of massive scalars from the complementary series in de Sitter space
• BRST quantization of the massless minimally coupled scalar field in de Sitter space (zero modes, euclideanization and quantization)
• The Fate of the Alpha-Vacuum
• Alpha-states in de Sitter space
• A de Sitter Hoedown
• de Sitter tachyons and related topics
• Scalar tachyons in the de Sitter universe
• Bootstrapping Massive Quantum Field Theories
• Tensors and Spinors in de Sitter Space
• Quasinormal Quantization in deSitter Spacetime
• (Non-)unitarity of strictly and partially massless fermions on de Sitter space
• An invitation to the principal series
• Group Averaging of massless scalar fields in 1+1 de Sitter

Cited by in corpus (13)

• On one-loop corrections to the Bunch-Davies wavefunction of the universe
• The Geometry of Cosmological Correlators
• Towards Systematic Evaluation of de Sitter Correlators via Generalized Integration-By-Parts Relations
• The Massive Flat Space Limit of Cosmological Correlators
• Multivariate hypergeometric solutions of cosmological (dS) correlators by $\text{d}\log$-form differential equations
• Bispectrum Islands
• Bananas are Unparticles: Differential Equations and Cosmological Bootstrap
• Charged Loops at the Cosmological Collider with Chemical Potential
• Hidden Conformal Symmetry of the Discrete Series Scalars in dS${}_2$
• Quantum information and the C-theorem in de Sitter
• RG flows in de Sitter: c-functions and sum rules
• Real-time observables in de Sitter thermodynamics
• Propagator positivity bounds for cosmological correlators