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Elements of Celestial Conformal Field Theory
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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.
Forward citations
Cited by 7 Pith papers
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Light and Shadow OPEs: A Carroll Symmetric Approach to Flat Holography
Translation symmetry alone fixes the scaling dimension and leading OPE coefficient for light-transformed Carrollian primaries, matching known graviton, gluon, and Einstein-Yang-Mills results.
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Conformal blocks from celestial graviton amplitudes
The authors construct a single-valued celestial four-graviton correlator from the shadow transform, decompose it into conformal blocks in all channels, and show it is the double copy of the corresponding gluon object.
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Worldsheet CFT$_2$ and Celestial CFT$_2$ : An AdS$_3$-CFT$_2$ perspective
A near-boundary scaling limit of AdS/CFT is proposed to produce celestial CFTs, and the long-string sector of string theory on AdS3 is identified as a Lorentz-only celestial CFT2.
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High Energy String Theory and the Celestial Sphere
The high-energy string amplitude and the celestial sphere amplitude share the same saddle point, and their subleading 1/alpha' and 1/beta corrections match order by order.
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Multiparticle States for the Flat Hologram
The paper defines and constructs composite or multiparticle primary operators for Carrollian and celestial CFTs using OPE blocks and momentum-space partial waves, extending the flat-space dictionary beyond single-part...
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The Sky Remembers everything: Celestial amplitude, Shadow and OPE in quadratic EFT of gravity
In quadratic gravity, celestial eikonal amplitudes are claimed to be meromorphic rather than distributional, with OPE data extracted from a shadowed correlator.
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Celestial Chiral Algebras and Self-Dual Gravity
This thesis derives deformations of celestial chiral algebras in self-dual gravity on curved backgrounds, obtaining W(infinity) on Eguchi-Hanson space, Ldiff_q(C) under Moyal deformation, and a two-parameter deformati...
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