Pith. sign in

REVIEW 5 cited by

The K\"all\'en-Lehmann representation in de Sitter spacetime

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2306.00090 v5 pith:BZI6I7MW submitted 2023-05-31 hep-th gr-qc

Manuel Loparco , Joao Penedones , Kamran Salehi Vaziri , Zimo Sun This is my paper · ORCID
classification hep-thgr-qc
keywords en-lehmannoperatorssitterspectraldecompositiondensitiesderivefunctions
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

We study two-point functions of symmetric traceless local operators in the bulk of de Sitter spacetime. We derive the K\"all\'en-Lehmann spectral decomposition for any spin and show that unitarity implies its spectral densities are nonnegative. In addition, we recover the K\"all\'en-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 K\"all\'en-Lehmann decomposition is useful to find the anomalous dimensions of the late-time boundary operators. We also derive the K\"all\'en-Lehmann representation of two-point functions of spinning primary operators of a Conformal Field Theory on de Sitter.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Ising the way into de Sitter

    hep-th 2026-07 conditional novelty 8.0 of 10

    The two-dimensional thermal Ising model on de Sitter provides exact cosmological correlators that stay finite at late times, with perturbative secular logarithms resummed into principal-series oscillations.

  2. On Cosmological Correlators at One Loop

    hep-th 2026-01 conditional novelty 8.0 of 10

    The one-loop triangle in-in correlator of massless scalars in flat space is evaluated in closed form in terms of dilogarithms, with Landau analysis revealing its physical singularities and a partial-energy factorisati...

  3. Propagator positivity bounds for cosmological correlators

    hep-th 2025-12 conditional novelty 7.0 of 10

    An infinite tower of two-sided positivity bounds constrains the EFT coefficients of heavy fields on de Sitter, ruling out correlators with no unitary/causal UV completion.

  4. Cosmological Correlators in Gauge Theory and Gravity from EAdS

    hep-th 2025-09 conditional novelty 6.0 of 10

    Gauge and gravitational late-time correlators in de Sitter are mapped to EAdS Witten diagrams, with new Mellin-space propagators and a treatment of even boundary dimensions.

  5. Cosmological correlators in gravitationally-constrained de Sitter states

    hep-th 2025-07 conditional novelty 6.0 of 10

    Cosmological correlators in gravitationally constrained de Sitter states are conformally invariant and differ from QFT vacuum correlators, but relational observables with a heavy background state can reproduce QFT results.

Pith tools