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.

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

References in corpus (7)

• Lectures on Celestial Amplitudes
• Holographic Symmetry Algebras for Gauge Theory and Gravity
• From Twistor Actions to MHV Diagrams
• Celestial Operator Product Expansions and ${\mathrm{w}}_{1+\infty }$ Symmetry for All Spins
• Twistor Actions for Self-Dual Supergravities
• Celestial operator products from the worldsheet
• Ambidextrous light transforms for celestial amplitudes

Cited by in corpus (31)

• Top-down holography in an asymptotically flat spacetime
• Celestial chiral algebras, colour-kinematics duality and integrability
• Celestial Amplitudes as AdS-Witten Diagrams
• The Celestial Chiral Algebra of Self-Dual Gravity on Eguchi-Hanson Space
• 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
• Celestial Leaf Amplitudes
• All-order celestial OPE in the MHV sector
• Celestial Locality and the Jacobi Identity
• Celestial Conformal Colliders
• The 4d/2d correspondence in twistor space and holomorphic Wilson lines
• Celestial Recursion
• 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
• Spectral representation in Klein space: simplifying celestial leaf amplitudes
• Celestial Gluon Amplitudes from the Outside In
• A General Hierarchy of Charges at Null Infinity via the Todd Polynomials
• Radiation in Fluid/Gravity and the Flat Limit
• One-loop corrections to the celestial chiral algebra from Koszul Duality
• Celestial $s{w}_{1+\infty }$ algebra in Einstein-Yang-Mills theory
• Loop corrections versus marginal deformation in celestial holography
• Celestial Quantum Error Correction II: From Qudits to Celestial CFT
• Supersymmetric String Configurations in Ad${\mathbb{S}}_5\times {\mathbb{S}}^5$