Ambidextrous light transforms for celestial amplitudes

Abstract

Low multiplicity celestial amplitudes of gluons and gravitons tend to be distributional in the celestial coordinates $z,\bar{z}$. We provide a new systematic remedy to this situation by studying celestial amplitudes in a basis of light transformed boost eigenstates. Motivated by a novel equivalence between light transforms and Witten's half-Fourier transforms to twistor space, we light transform every positive helicity state in the coordinate $z$ and every negative helicity state in $\bar{z}$. With examples, we show that this "ambidextrous" prescription beautifully recasts two- and three-point celestial amplitudes in terms of standard conformally covariant structures. These are used to extract examples of celestial OPE for light transformed operators. We also study such amplitudes at higher multiplicity by constructing the Grassmannian representation of tree-level gluon celestial amplitudes as well as their light transforms. The formulae for $n$-point N${}^{k-2}$MHV amplitudes take the form of Euler-type integrals over regions in Gr$(k,n)$ cut out by positive energy constraints.

30 pages, no figures; v2 published version

References in corpus (19)

• Gluon Amplitudes as 2d Conformal Correlators
• Holographic Symmetry Algebras for Gauge Theory and Gravity
• Celestial Amplitudes from UV to IR
• Perturbative gravity at null infinity
• Ambitwistor strings at null infinity and subleading soft limits
• $(2,2)$ Scattering and the Celestial Torus
• Celestial Diamonds: Conformal Multiplets in Celestial CFT
• Conformal Block Expansion in Celestial CFT
• Shifting Spin on the Celestial Sphere
• Revisiting the Conformally Soft Sector with Celestial Diamonds
• MHV Gluon Scattering Amplitudes from Celestial Current Algebras
• Conformal Blocks from Celestial Gluon Amplitudes
• Perturbative gauge theory at null infinity
• Notes on Conformal Soft Theorems and Recursion Relations in Gravity
• State-Operator Correspondence in Celestial Conformal Field Theory
• Celestial double copy from the worldsheet
• Celestial Dual Superconformal Symmetry, MHV Amplitudes and Differential Equations
• Celestial Superamplitudes
• w(1+infinity) and the Celestial Sphere

Cited by in corpus (20)

• Celestial Operator Product Expansions and ${\mathrm{w}}_{1+\infty }$ Symmetry for All Spins
• Celestial holography meets twisted holography: 4d amplitudes from chiral correlators
• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
• Goldilocks Modes and the Three Scattering Bases
• Celestial $w_{1+\infty }$ Symmetries from Twistor Space
• Conformal Blocks from Celestial Gluon Amplitudes II: Single-valued Correlators
• Black Holes in Klein Space
• Four-point correlators of light-ray operators in CCFT
• Celestial Locality and the Jacobi Identity
• Revisiting the Shadow Stress Tensor in Celestial CFT
• Towards higher-spin holography in flat space
• Shadow Celestial Amplitude
• (Chiral) Virasoro invariance of the tree-level MHV graviton scattering amplitudes
• Celestial amplitudes in an ambidextrous basis
• Celestial Geometry
• The Grassmannian for Celestial Superamplitudes
• Missing Corner in the Sky: Massless Three-Point Celestial Amplitudes
• Light transformed gluon correlators in CCFT
• Mapping SYK to the Sky
• Celestial OPE blocks