Celestial holography meets twisted holography: 4d amplitudes from chiral correlators

Abstract

We propose a new program for computing a certain integrand of scattering amplitudes of four-dimensional gauge theories which we call the \textit{form factor integrand}, starting from 6d holomorphic theories on twistor space. We show that the form factor integrands can be expressed as sums of products of 1.) correlators of a 2d chiral algebra, related to the algebra of asymptotic symmetries uncovered recently in the celestial holography program, and 2.) OPE coefficients of a 4d non-unitary CFT. We prove that conformal blocks of the chiral algebras are in one-to-one correspondence with local operators in 4d. We use this bijection to recover the Parke-Taylor formula, the CSW formula, and certain one-loop scattering amplitudes. Along the way, we explain and derive various aspects of celestial holography, incorporating techniques from the twisted holography program such as Koszul duality. This perspective allows us to easily and efficiently recover the infinite-dimensional chiral algebras of asymptotic symmetries recently extracted from scattering amplitudes of massless gluons and gravitons in the celestial basis. We also compute some simple one-loop corrections to the chiral algebras and derive the three-dimensional bulk theories for which these 2d algebras furnish an algebra of boundary local operators.

arXiv comment82 pages, 6 figures, 1 table. Version 2: several corrections, more one-loop amplitudes computed. v3: minor corrections, JHEP published version

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• From Moyal deformations to chiral higher-spin theories and to celestial algebras
• Deforming Soft Algebras for Gauge Theory
• On the associativity of 1-loop corrections to the celestial operator product in gravity
• A Comment on Loop Corrections to the Celestial Stress Tensor
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• Celestial Locality and the Jacobi Identity
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• Celestial amplitudes in an ambidextrous basis
• Celestial Supersymmetry
• Lorentz Symmetry and IR Structure of The BFSS Matrix Model
• All-order celestial OPE from on-shell recursion
• Detector Operators for Celestial Symmetries
• Integrable Field Theories and Their CCFT Duals
• The $\mathcal{N}=2$ Supersymmetric $w_{1+\infty }$ Symmetry in the Two-Dimensional SYK Models
• An On-Shell Derivation of the Soft Effective Action in Abelian Gauge Theories
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• Celestial Gluon Amplitudes from the Outside In
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• Supersymmetric String Configurations in Ad${\mathbb{S}}_5\times {\mathbb{S}}^5$