Four-point correlators of light-ray operators in CCFT

Hu, Yangrui; Lippstreu, Luke; Spradlin, Marcus; Srikant, Akshay Yelleshpur; Volovich, Anastasia

doi:10.1007/jhep07(2022)104

Cited by 22 publications

(34 citation statements)

References 40 publications

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“…These amount to stripping off different kinematical factors. More explicitly, the choice of Ω i in (3.34) is appropriate for the canonical form (3.5), used here and in [25,36,43], while other choices of kinematical factors are common in the CFT literature and can be useful for examining the celestial conformal block decomposition [20,[47][48][49][50][51].…”

Section: Jhep09(2022)045mentioning

confidence: 99%

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Celestial geometry

Mizera

Pasterski

2022

J. High Energ. Phys.

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Celestial holography expresses $$ \mathcal{S} $$ S -matrix elements as correlators in a CFT living on the night sky. Poincaré invariance imposes additional selection rules on the allowed positions of operators. As a consequence, n-point correlators are only supported on certain patches of the celestial sphere, depending on the labeling of each operator as incoming/outgoing. Here we initiate a study of the celestial geometry, examining the kinematic support of celestial amplitudes for different crossing channels. We give simple geometric rules for determining this support. For n ≥ 5, we can view these channels as tiling together to form a covering of the celestial sphere. Our analysis serves as a stepping off point to better understand the analyticity of celestial correlators and illuminate the connection between the 4D kinematic and 2D CFT notions of crossing symmetry.

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Section: Jhep09(2022)045mentioning

confidence: 99%

“…Most likely, a good notion of holomorphic factorization, or conformal-block decomposition, will be needed. For recent progress on CCFT conformal blocks, see, e.g., [20,[47][48][49][50][51].…”

Section: Jhep09(2022)045mentioning

confidence: 99%

Celestial geometry

Mizera

Pasterski

2022

J. High Energ. Phys.

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“…In the second approach, we can remedy the singular delta function behavior by performing the light transformation [32] or shadow transformation [33] on some operators in (4.6). The integral transformation would remove the delta function in (4.9), 15 and the corresponding four point function would be very well behaved.…”

Section: Comments On Higher-dimensional Generalizationsmentioning

confidence: 99%

Celestial Mellin Amplitude

Jiang¹

2022

Preprint

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Celestial holography provides a promising avenue to studying bulk scattering in flat spacetime from the perspective of boundary celestial conformal field theory (CCFT). A key ingredient in connecting the two sides is the celestial amplitude, which is given by the Mellin transform of momentum space scattering amplitude in energy. As such, celestial amplitudes can be identified with the correlation functions in celestial conformal field theory. In this paper, we introduce the further notion of celestial Mellin amplitude, which is given by the Mellin transform of celestial amplitude in coordinate. For technical reasons, we focus on the celestial Mellin amplitudes for scalar fields in three dimensional flat spacetime dual to 1D CCFT, and discuss the celestial Mellin block expansion. In particular, the poles of the celestial Mellin amplitude encode the scaling dimensions of the possible exchanged operators, while the residues there are related to the OPE coefficient squares in a linear and explicit way. We also compare the celestial Mellin amplitudes with the coefficient functions which can be obtained using inversion formulae. Finally, we make some comments about the possible generalizations of celestial Mellin amplitudes to higher dimensions.

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“…1 However, since the integration kernel in the conformal partial wave expansion does not have poles located at the right half-plane, one does not get a conformal block expansion by closing the contour. Again, in the literature, the studies of conformal block expansion of celestial amplitudes are limited to the Klein space [28][29][30][31] or three dimensional space [32,33].…”

Section: B the Conformal Integral 1 Introductionmentioning

confidence: 99%

Shadow Celestial Amplitude

Chang¹,

Cui²,

Ma³

et al. 2022

Preprint

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We study scattering amplitudes in the shadow conformal primary basis, which satisfies the same defining properties as the original conformal primary basis and has many advantages over it. The shadow celestial amplitudes exhibit locality manifestly on the celestial sphere, and behave like correlation functions in conformal field theory under the operator product expansion (OPE) limit. We study the OPE limits for three-point shadow celestial amplitude, and general 2 → n − 2 shadow celestial amplitudes from a large class of Feynman diagrams. In particular, we compute the conformal block expansion of the s-channel four-point shadow celestial amplitude of massless scalars at tree-level, and show that the expansion coefficients factorize as products of OPE coefficients.

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Four-point correlators of light-ray operators in CCFT

Cited by 22 publications

References 40 publications

Celestial geometry

Celestial geometry

Celestial Mellin Amplitude

Shadow Celestial Amplitude

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