Celestial amplitudes in an ambidextrous basis

Abstract

We start by constructing a conformally covariant improvement of the celestial light transform which keeps track of the mixing between incoming and outgoing states under finite Lorentz transformations in ${\mathbb{R}}^{2,2}$. We then compute generic 2, 3 and 4-point celestial amplitudes for massless external states in the ambidextrous basis prepared by composing this $\mathrm{SL}(2,\mathbb{R})$ intertwiner with the usual celestial map between momentum and boost eigenstates. The results are non-distributional in the celestial coordinates $(z,\bar{z})$ and conformally covariant in all scattering channels. Finally, we focus on the tree level 4-gluon amplitude where we present a streamlined route to the ambidextrous correlator based on Grassmannian formulae and examine its alpha space representation. In the process, we gain insights into the operator dictionary and CFT data of the holographic dual.

arXiv comment55 pages, 3 figures

References in corpus (45)

• Perturbative Gauge Theory As A String Theory In Twistor Space
• BMS supertranslations and Weinberg's soft graviton theorem
• Analyticity in Spin in Conformal Theories
• A Duality For The S Matrix
• Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere
• A Conformal Basis for Flat Space Amplitudes
• A holographic reduction of Minkowski space-time
• Light-ray operators in conformal field theory
• Gluon Amplitudes as 2d Conformal Correlators
• A 2D Stress Tensor for 4D Gravity
• Holographic Symmetry Algebras for Gauge Theory and Gravity
• 4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT
• A spacetime derivation of the Lorentzian OPE inversion formula
• The S-Matrix in Twistor Space
• Conformally Soft Photons and Gravitons
• Asymptotic Symmetries and Celestial CFT
• Celestial Amplitudes from UV to IR
• Celestial holography meets twisted holography: 4d amplitudes from chiral correlators
• Celestial Amplitudes: Conformal Partial Waves and Soft Limits
• Extended BMS Algebra of Celestial CFT
• Crossing Symmetry in Alpha Space
• $(2,2)$ Scattering and the Celestial Torus
• Conformal Basis, Optical Theorem, and the Bulk Point Singularity
• Conformal Block Expansion in Celestial CFT
• Scattering Amplitudes and BCFW Recursion in Twistor Space
• Shifting Spin on the Celestial Sphere
• Revisiting the Conformally Soft Sector with Celestial Diamonds
• Conformal Blocks from Celestial Gluon Amplitudes
• Primary Fields in Celestial CFT
• Celestial operator products from the worldsheet
• State-Operator Correspondence in Celestial Conformal Field Theory
• Elements of Celestial Conformal Field Theory
• Ambidextrous light transforms for celestial amplitudes
• Goldilocks Modes and the Three Scattering Bases
• Relativistic partial waves for celestial amplitudes
• Conformal Blocks from Celestial Gluon Amplitudes II: Single-valued Correlators
• On the associativity of 1-loop corrections to the celestial operator product in gravity
• Four-point correlators of light-ray operators in CCFT
• Notes on Resonances and Unitarity from Celestial Amplitudes
• The 4d/2d correspondence in twistor space and holomorphic Wilson lines
• Celestial Geometry
• Correlators of Four Light-Ray Operators in CCFT
• The Grassmannian for Celestial Superamplitudes
• Light transformed gluon correlators in CCFT
• Applications of Alpha Space

Cited by in corpus (4)

• All-order celestial OPE from on-shell recursion
• Missing Corner in the Sky: Massless Three-Point Celestial Amplitudes
• Multiparticle Contributions to the Celestial OPE
• Celestial Regge theory