Cosmological Scattering Equations at Tree-level and One-loop

Gomez, Humberto; Jusinskas, Renann Lipinski; Lipstein, Arthur

doi:10.48550/arxiv.2112.12695

Cited by 5 publications

(7 citation statements)

References 94 publications

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“…Obviously, much of our discussion has leaned heavily on equations of motion for computing the classical sector of the dynamics. It would be interesting to see if this can be extended, perhaps in line with recent work in AdS [96] and dS [97]. A closely related question is whether the machinery we have presented can be used to compute off-shell correlators, corresponding to processes with local insertions of a source.…”

Section: Discussionmentioning

confidence: 66%

On-shell correlators and color-kinematics duality in curved symmetric spacetimes

Cheung

Parra-Martinez

Sivaramakrishnan

2022

J. High Energ. Phys.

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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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Section: Discussionmentioning

confidence: 66%

On-shell correlators and color-kinematics duality in curved symmetric spacetimes

Cheung

Parra-Martinez

Sivaramakrishnan

2022

J. High Energ. Phys.

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“…Worldsheet correlators of these models then compute amplitudes around such backgrounds. The feasibility of using ambitwistor strings to compute amplitudes has been demonstrated on plane wave backgrounds at three points [141], and in (A)dS backgrounds at general multiplicity for certain theories [142][143][144][145]. It would be interesting to pursue this approach to build scattering equations and worldsheet formulae for amplitudes on other space-times of interest.…”

Section: Discussionmentioning

confidence: 99%

Graviton scattering in self-dual radiative space-times

Adamo¹,

Mason²,

Sharma³

2022

Preprint

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We give formulae for all tree-level graviton scattering amplitudes in curved self-dual radiative space-times; these are chiral, source-free, asymptotically flat spaces determined by free characteristic data at null infinity. Such space-times admit an elegant description in terms of twistor theory and Penrose's non-linear graviton, which manifests their underlying integrability. The tree-level S-matrix is written in terms of an integral over the moduli space of holomorphic maps from the Riemann sphere to twistor space, with the degree of the map corresponding to the helicity configuration of the external gravitons. For the MHV sector, we derive the amplitude directly from general relativity, while other helicity configurations arise from a natural family of generating functionals and pass several consistency checks. The amplitudes in self-dual radiative space-times exhibit many novel features which are absent in Minkowski space, including tail effects. There are also residual integrals due to the functional degrees of freedom in the background space-time, although our formulae have fewer such integrals than expected from space-time perturbation theory. In highly symmetric special cases, such as self-dual plane waves, the number of residual integrals can be further reduced, resulting in even simpler expressions for the scattering amplitudes.

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“…The construction described in this paper extends without difficulty to the other maximally-symmetric space, such as the de Sitter space (see [47,50] for earlier work in this direction). Furthermore, a somewhat similar formalism was developed in refs.…”

Section: Jhep05(2022)026mentioning

confidence: 98%

“…1 It thus naturally manifests all symmetries, encompasses all of the various representations (position, momentum and Mellin), and may expose structures hidden under these traditional representations, such as the existence [44] of differential relations between color-ordered boundary correlators analogous to the flat space Bern-Carrasco-Johansson (BCJ) amplitudes relations [45]. Beyond tree level, the differential representation has proven useful for evaluating scalar one-loop Witten diagrams in both AdS [46] and dS [47]. Originally motivated by the infinite tension limit of certain string theory expressions for scalar external states [48,49], the differential representation parallels many features of the momentum-JHEP05(2022)026 space representation of flat-space scattering amplitudes [44], see also [50,51].…”

Section: Jhep05(2022)026mentioning

confidence: 99%

“…19 If sufficiently precise, the notion of "factorization on D i 1 ...i k = −M 2 pole" foreshadows a new formulation 20 of on-shell recursion relations [81] in AdS as well as a differential formulation 21 of the generalized unitarity method [88][89][90][91][92]. Together with a notion of integration over the space of conformal generators, along the lines of [46,47], it may lead to new approaches to loop-level AdS boundary correlators.…”

Section: Jhep05(2022)026mentioning

confidence: 99%

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On the differential representation and color-kinematics duality of AdS boundary correlators

Herderschee

Roiban

Teng

2022

J. High Energ. Phys.

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The AdS boundary correlators and their dual correlation functions of boundary operators have been the main dynamic observables of the holographic duality relating a bulk AdS theory and a boundary conformal field theory. We show that tree-level AdS boundary correlators for generic states can be expressed as nonlocal differential operators of a certain structure acting on contact Witten diagrams. We further write the boundary correlators in a form that is very similar to flat space amplitudes, with Mandelstam variables replaced by certain combinations of single-state conformal generators, prove that all tree-level AdS boundary correlators have a differential representation, and detail the conversion of such differential expressions to position space. We illustrate the construction through the computation of the boundary correlators of scalars coupled to gluons and gravitons; when converted to position space, they reproduce known results. Color-kinematics duality and BCJ relations can be defined in analogy with their flat space counterparts, and are respected by the scalar correlators with a gluon exchange. We also discuss potential approaches to the double copy and find that its direct generalization may require nontrivial extensions.

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Cosmological Scattering Equations at Tree-level and One-loop

Cited by 5 publications

References 94 publications

On-shell correlators and color-kinematics duality in curved symmetric spacetimes

On-shell correlators and color-kinematics duality in curved symmetric spacetimes

Graviton scattering in self-dual radiative space-times

On the differential representation and color-kinematics duality of AdS boundary correlators

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