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1. Conformal blocks from celestial gluon amplitudes

   https://doi.org/10.1007/JHEP05(2021)170  

   Fan, Wei; Fotopoulos, Angelos; Stieberger, Stephan; Taylor, Tomasz R.; Zhu, Bin (May 2021, Journal of High Energy Physics)

   null (Ed.)

   A bstract In celestial conformal field theory, gluons are represented by primary fields with dimensions ∆ = 1 + iλ , λ ∈ ℝ and spin J = ±1, in the adjoint representation of the gauge group. All two- and three-point correlation functions of these fields are zero as a consequence of four-dimensional kinematic constraints. Four-point correlation functions contain delta-function singularities enforcing planarity of four-particle scattering events. We relax these constraints by taking a shadow transform of one field and perform conformal block decomposition of the corresponding correlators. We compute the conformal block coefficients. When decomposed in channels that are “compatible” in two and four dimensions, such four-point correlators contain conformal blocks of primary fields with dimensions ∆ = 2 + M + iλ , where M ≥ 0 is an integer, with integer spin J = −M, −M + 2 , … , M − 2 , M . They appear in all gauge group representations obtained from a tensor product of two adjoint representations. When decomposed in incompatible channels, they also contain primary fields with continuous complex spin, but with positive integer dimensions. 

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2. Elements of celestial conformal field theory

   https://doi.org/10.1007/JHEP08(2022)213  

   Fan, Wei; Fotopoulos, Angelos; Stieberger, Stephan; Taylor, Tomasz R.; Zhu, Bin (August 2022, Journal of High Energy Physics)

   A bstract 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. 

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3. Partially celestial states and their scattering amplitudes

   https://doi.org/10.1103/PhysRevD.109.105020  

   Csáki, Csaba; Telem, Ofri; Terning, John (May 2024, Physical Review D)

   We study representations of the Poincaré group that have a privileged transformation law along a $p$-dimensional hyperplane, and uncover their associated spinor-helicity variables in $D$spacetime dimensions. Our novel representations generalize the recently introduced celestial states and transform as conformal primaries of $SO(p,1)$, the symmetry group of the $p$-hyperplane. We will refer to our generalized states as “partially celestial.” Following Wigner’s method, we find the induced representations, including spin degrees of freedom. Defining generalized spinor-helicity variables for every $D$and $p$, we are able to construct the little group covariant part of partially celestial amplitudes. Finally, we briefly examine the application of the pairwise little group to partially celestial states with mutually nonlocal charges. Published by the American Physical Society2024 

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4. Yang-Mills as a Liouville theory

   https://doi.org/10.1016/j.physletb.2023.138229  

   Stieberger, Stephan; Taylor, Tomasz R; Zhu, Bin (November 2023, Physics Letters B)

   We propose a description of the gluon scattering amplitudes as the inverse Mellin transforms of the conformal correlators of light operators in two-dimensional Liouville theory tensored with WZW-like chiral currents on the celestial sphere. The dimensions of operators are Mellin dual to gluon light cone energies while their positions are determined by the gluon momentum directions. Tree-level approximation in Yang-Mills theory corresponds to the semiclassical limit of Liouville theory. By comparing subleading corrections, we find b^2=(8π^2)^{−1}b_0g^2(M), where b is the Liouville coupling constant, g(M) is the Yang Mills coupling at the renormalization scale M and b_0 is the one-loop coefficient of the Yang-Mills beta function. 

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5. Celestial gluon and graviton OPE at loop level

   https://doi.org/10.1007/JHEP03(2024)176  

   Krishna, Hare (March 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> In this paper, we analyze the loop corrections to celestial OPE for gluons and gravitons. Even at the loop level, the soft gluons and gravitons have conformal dimensions ∆ = 1−$${\mathbb{Z}}_{\ge 0}$$. The only novelty is the presence of higher poles. At one loop level, there are two types of conformal soft gluons with a single pole and a double pole in the ∆ plane. The celestial OPEs are obtained using the collinear splitting functions. In the case of gluons, the splitting functions receive loop corrections. After taking the holomorphic soft limit, we find the OPE of conformal soft gluons. We find a novel mixing of simple and double poles soft gluon operators in the OPE. In the case of gravitons, where splitting functions are known to be all loop exact, we still find a wedge algebra ofw_∞which is in addition to the wedge algebra ofw_1+∞already found by Strominger. 

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