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1. Descendants in celestial CFT and emergent multi-collinear factorization

   https://doi.org/10.1007/JHEP03(2021)030  

   Ebert, Stephen; Sharma, Atul; Wang, Diandian (March 2021, Journal of High Energy Physics)

   null (Ed.)

   A bstract Multi-collinear factorization limits provide a window to study how locality and unitarity of scattering amplitudes can emerge dynamically from celestial CFT, the conjectured holographic dual to gauge and gravitational theories in flat space. To this end, we first use asymptotic symmetries to commence a systematic study of conformal and Kac-Moody descendants in the OPE of celestial gluons. Recursive application of these OPEs then equips us with a novel holographic method of computing the multi-collinear limits of gluon amplitudes. We perform this computation for some of the simplest helicity assignments of the collinear particles. The prediction from the OPE matches with Mellin transforms of the expressions in the literature to all orders in conformal descendants. In a similar vein, we conclude by studying multi-collinear limits of graviton amplitudes in the leading approximation of sequential double-collinear limits, again finding a consistency check against the leading order OPE of celestial gravitons. 

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2. 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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3. Celestial operator products of gluons and gravitons

   https://doi.org/10.1142/9789811210679_0020  

   Pate, Monica; Raclariu, Ana-Maria; Strominger, Andrew; Ye Yuan, Ellis (October 2019, ArXivorg)

   null (Ed.)

   The operator product expansion (OPE) on the celestial sphere of conformal primary gluons and gravitons is studied. Asymptotic symmetries imply recursion relations between products of operators whose conformal weights differ by half-integers. It is shown, for tree-level Einstein-Yang-Mills theory, that these recursion relations are so constraining that they completely fix the leading celestial OPE coefficients in terms of the Euler beta function. The poles in the beta functions are associated with conformally soft currents. 

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4. Collinear anatomy

   https://doi.org/10.1007/JHEP05(2025)117  

   Belitsky, AV (May 2025, Journal of High Energy Physics)

   A<sc>bstract</sc> We study the collinear factorization of off-shell scattering amplitudes in maximally supersymmetric Yang-Mills (sYM) theory. These are constructed starting from six-dimensional$$ \mathcal{N} $$ $N$= (1) sYM, taking advantage of an available unconstrained spinor-helicity formalism combined with a unitarity-cut sewing procedure. After generalized dimensional reduction, their collinear behavior is dissected with assistance from the Method of Regions. We then construct off-shell splitting amplitudes directly using the same techniques, establishing equivalence to the amplitude analysis. The calculations are performed at one-loop order. 

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5. Generalized Veneziano and Virasoro amplitudes

   https://doi.org/10.1007/JHEP04(2023)031  

   Geiser, Nicholas; Lindwasser, Lukas W. (April 2023, Journal of High Energy Physics)

   A<sc>bstract</sc> We analyze so-called generalized Veneziano and generalized Virasoro amplitudes. Under some physical assumptions, we find that their spectra must satisfy an over-determined set of non-linear recursion relations. The recursion relation for the generalized Veneziano amplitudes can be solved analytically and yields a two-parameter family which includes the Veneziano amplitude, the one-parameter family of Coon amplitudes, and a larger two-parameter family of amplitudes with an infinite tower of spins at each mass level. In the generalized Virasoro case, the only consistent solution is the string spectrum. 

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