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From dS to AdS and back
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We describe in more detail the general relation uncovered in our previous work between boundary correlators in de Sitter (dS) and in Euclidean anti-de Sitter (EAdS) space, at any order in perturbation theory. Assuming the Bunch-Davies vacuum at early times, any given diagram contributing to a boundary correlator in dS can be expressed as a linear combination of Witten diagrams for the corresponding process in EAdS, where the relative coefficients are fixed by consistent on-shell factorisation in dS. These coefficients are given by certain sinusoidal factors which account for the change in coefficient of the contact sub-diagrams from EAdS to dS, which we argue encode (perturbative) unitary time evolution in dS. dS boundary correlators with Bunch-Davies initial conditions thus perturbatively have the same singularity structure as their Euclidean AdS counterparts and the identities between them allow to directly import the wealth of techniques, results and understanding from AdS to dS. This includes the Conformal Partial Wave expansion and, by going from single-valued Witten diagrams in EAdS to Lorentzian AdS, the Froissart-Gribov inversion formula. We give a few (among the many possible) applications both at tree and loop level. Such identities between boundary correlators in dS and EAdS are made manifest by the Mellin-Barnes representation of boundary correlators, which we point out is a useful tool in its own right as the analogue of the Fourier transform for the dilatation group. The Mellin-Barnes representation in particular makes manifest factorisation and dispersion formulas for bulk-to-bulk propagators in (EA)dS, which imply Cutkosky cutting rules and dispersion formulas for boundary correlators in (EA)dS. Our results are completely general and in particular apply to any interaction of (integer) spinning fields.
Forward citations
Cited by 14 Pith papers
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Higher-Spin Correlators in dS
The five-point de Sitter higher-spin correlator is shown to be a spurious-singularity-free rational function organized by graph-theoretic orbits of the complete graph K5.
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All Tree-Level Massive Cosmological Correlators via Spectral Gluing
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Propagator positivity bounds for cosmological correlators
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Conformal Partial Wave Expansion of Celestial Correlators
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Massive Inflationary Amplitudes: Differential Equations and Complete Solutions for General Trees
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From Cosmological Cuts to Yang--Mills Wavefunctions in de Sitter Space
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Cosmological Correlators in Gauge Theory and Gravity from EAdS
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.
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A non-perturbative construction of the de Sitter late-time boundary
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Cosmological Correlators at the Loop Level
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Cosmological Cutting Rules from Flat-Space Unitarity via Dressing
Flat-space Cutkosky cuts, after cosmological dressing and analytic continuation, become the Disc operations appearing in dS/EAdS cosmological cutting rules.
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Integrable models of inflation beyond slow-roll
Integrable inflationary models built from a chosen Hubble function yield power spectra, spectral indices, and tensor-to-scalar ratios, computed beyond slow-roll, that match currently available CMB data.
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EFT Perspective On de-Sitter S-Matrix
In a carefully chosen limit, the de Sitter scattering amplitude is written as an integral transform of the flat-space amplitude, and requiring energy conservation on exceptional de Sitter scalars reproduces DBI and Sp...
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