Analyticity and unitarity for cosmological correlators

Pietro, Lorenzo Di; Gorbenko, V.; Komatsu, Shota

doi:10.1007/jhep03(2022)023

Cited by 96 publications

(102 citation statements)

References 144 publications

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“…The most interesting question is perhaps how best to extract constraints on inflationary observables; see e.g. [190][191][192][193][194][195][196][197][198][199][200][201][202][203] for recent steps in this direction.…”

Section: Bootstrapping Holographic Duality Beyond Ads/cftmentioning

confidence: 99%

Snowmass White Paper: The Analytic Conformal Bootstrap

Hartman¹,

Mazáč²,

Simmons-Duffin³

et al. 2022

Preprint

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The analytic conformal bootstrap is an array of techniques to characterize, constrain, and solve strongly interacting quantum field theories using symmetries, causality, unitarity, and other general principles. In the last decade, bolstered by the development of new Lorentzian methods, it has been used to solve conformal field theories at large spin; to place bounds on energy distributions, event shapes, operator product coefficients, and other observables; and to understand aspects of quantum gravity in anti-de Sitter space. We review these advances and highlight several promising areas for future exploration. Targets include developing new methods to close the gap between numerical and analytic bounds, extending the bootstrap beyond conformal fixed points, applications to quantum gravity and cosmology, and building on ties to condensed matter theory and mathematics.

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Section: Bootstrapping Holographic Duality Beyond Ads/cftmentioning

confidence: 99%

Snowmass White Paper: The Analytic Conformal Bootstrap

Hartman¹,

Mazáč²,

Simmons-Duffin³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…For recent work on analytic continuations from AdS to dS, see [46-48, 56, 62]. Our results may be useful for bootstrapping dS quantities in concert with the methods in [55,64,[104][105][106]. Isometric kinematics may simplify aspects of momentum-space computations in dS.…”

Section: Discussionmentioning

confidence: 81%

“…Of course, many advances in this direction have been made for maximally symmetric spaces, namely anti-de Sitter (AdS) space and de Sitter (dS) space. Ongoing explorations of Mellin space [41][42][43][44][45][46][47][48], transition amplitudes [49][50][51], harmonic analysis [52][53][54][55][56], and unitarity [57][58][59][60][61][62][63][64][65][66][67][68] have all identified various notions of simplified and on-shell kinematics for curved spacetime.…”

Section: Introductionmentioning

confidence: 99%

On-shell Correlators and Color-Kinematics Duality in Curved Symmetric Spacetimes

Cheung,

Parra-Martinez,

Sivaramakrishnan

2022

Preprint

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We define a perturbatively calculable quantity-the on-shell correlator-which furnishes a unified description of particle dynamics in curved spacetime. Specializing to the case of flat and anti-de Sitter space, on-shell correlators coincide precisely with on-shell scattering amplitudes and boundary correlators, respectively. Remarkably, we find that symmetric manifolds admit a generalization of on-shell kinematics in which the corresponding momenta are literally the isometry generators of the spacetime acting on the external kinematic data. These isometric momenta are intrinsically non-commutative but exhibit on-shell conditions that are identical to those of flat space, thus providing a common language for computing and representing on-shell correlators which is agnostic about the underlying geometry. Afterwards, we compute tree-level on-shell correlators for biadjoint scalar (BAS) theory and the nonlinear sigma model (NLSM) and learn that color-kinematics duality is manifested at the level of fields under a mapping of the color algebra to the algebra of gauged isometries on the spacetime manifold. Last but not least, we present a field theoretic derivation of the fundamental BCJ relations for on-shell correlators following from the existence of certain conserved currents in BAS theory and the NLSM.

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“…Finally, we would like to mention some recent developments in the calculation of cosmological correlators in de Sitter [36,[83][84][85]. It could be interesting to explore, if our method can be applied in that framework as well.…”

Section: Discussionmentioning

confidence: 99%

Analytical evaluation of AdS${}_4$ Witten diagrams as flat space multi-loop Feynman integrals

Heckelbacher¹,

Sachs²,

Skvortsov³

et al. 2022

Preprint

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We describe a systematic approach for the evaluation of Witten diagrams for multi-loop scattering amplitudes of a conformally coupled scalar φ 4 -theory in Euclidean AdS 4 , by recasting the Witten diagrams as flat space Feynman integrals. We derive closed form expressions for the anomalous dimensions for all double-trace operators up to the second order in the coupling constant. We explain the relation between the flat space unitarity methods and the discontinuities of the short distance expansion on the boundary of Witten diagrams. B Evaluation of the Witten cross diagram B.1 The analytic evaluation of cross diagram for all ∆ B.2 Cross in dimensional regularisation B.3 The expansion of the cross diagram C Evaluation of the one-loop Witten bubble diagram C.1 The one-loop diagram C.1.1 ∆ = 1 C.1.2 ∆ = 2 C.1.3 L ∆ 0 integrals C.1.4 L ′ 0 integrals C.2 Expressions from unitarity cuts D Conformal blocks and OPE coefficients

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Analyticity and unitarity for cosmological correlators

Cited by 96 publications

References 144 publications

Snowmass White Paper: The Analytic Conformal Bootstrap

Snowmass White Paper: The Analytic Conformal Bootstrap

On-shell Correlators and Color-Kinematics Duality in Curved Symmetric Spacetimes

Analytical evaluation of AdS${}_4$ Witten diagrams as flat space multi-loop Feynman integrals

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