Elements of Celestial Conformal Field Theory

Abstract

In celestial holography, four-dimensional scattering amplitudes are considered as two-dimensional conformal correlators of a putative two-dimensional celestial conformal field theory (CCFT). The simplest way of converting momentum space amplitudes into CCFT correlators is by taking their Mellin transforms with respect to light-cone energies. For massless particles, like gluons, however, such a construction leads to three-point and four-point correlators that vanish everywhere except for a measure zero hypersurface of celestial coordinates. This is due to the four-dimensional momentum conservation law that constrains the insertion points of the operators associated with massless particles. These correlators are reminiscent of Coulomb gas correlators that, in the absence of background charges, vanish due to charge conservation. We supply the background momentum by coupling Yang-Mills theory to a background dilaton field, with the (complex) dilaton source localized on the celestial sphere. This picture emerges from the physical interpretation of the solutions of the system of differential equations discovered by Banerjee and Ghosh. We show that the solutions can be written as Mellin transforms of the amplitudes evaluated in such a dilaton background. The resultant three-gluon and four-gluon amplitudes are single-valued functions of celestial coordinates enjoying crossing symmetry and all other properties expected from standard CFT correlators. We use them to extract OPEs and compare them with the OPEs extracted from multi-gluon celestial amplitudes without a dilaton background. We perform the conformal block decomposition of the four-gluon single-valued correlator and determine the dimensions, spin and group representations of the entire primary field spectrum of the Yang-Mills sector of CCFT.

32 pages

References in corpus (4)

• Gluon Amplitudes as 2d Conformal Correlators
• Symmetries of Celestial Amplitudes
• New Relations for Einstein-Yang-Mills Amplitudes
• Lectures on Celestial Holography

Cited by in corpus (19)

• Top-down holography in an asymptotically flat spacetime
• Celestial Amplitudes as AdS-Witten Diagrams
• Celestial holography on Kerr-Schild backgrounds
• Celestial Liouville Theory for Yang-Mills Amplitudes
• Deforming Soft Algebras for Gauge Theory
• Soft Scalars and the Geometry of the Space of Celestial CFTs
• Four-point correlators of light-ray operators in CCFT
• Celestial Locality and the Jacobi Identity
• Celestial Leaf Amplitudes
• Celestial Yang-Mills Amplitudes and D=4 Conformal Blocks
• Celestial Supersymmetry
• Celestial amplitudes in an ambidextrous basis
• Celestial Recursion
• Celestial Geometry
• Spectral representation in Klein space: simplifying celestial leaf amplitudes
• Soft and Collinear Limits in $\mathcal{N}=8$ Supergravity using Double Copy Formalism
• Celestial Gluon Amplitudes from the Outside In
• The Sky Remembers everything: Celestial amplitude, Shadow and OPE in quadratic EFT of gravity
• Entanglement Rényi entropies in celestial holography