Celestial Operator Product Expansions and ${\mathrm{w}}_{1+\infty }$ Symmetry for All Spins

Abstract

The operator product expansion of massless celestial primary operators of arbitrary spin is investigated. Poincaré symmetry is found to imply a set of recursion relations on the operator product expansion coefficients of the leading singular terms at tree-level in a holomorphic limit. The symmetry constraints are solved by an Euler beta function with arguments that depend simply on the right-moving conformal weights of the operators in the product. These symmetry-derived coefficients are shown not only to match precisely those arising from momentum-space tree-level collinear limits, but also to obey an infinite number of additional symmetry transformations that respect the algebra of ${\mathrm{w}}_{1+\infty }$. In tree-level minimally-coupled gravitational theories, celestial currents are constructed from light transforms of conformally soft gravitons and found to generate the action of ${\mathrm{w}}_{1+\infty }$ on arbitrary massless celestial primaries. Results include operator product expansion coefficients for fermions as well as those arising from higher-derivative non-minimal couplings of gluons and gravitons.

26 pages. In v2: references added, discussion of EFT corrections corrected

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• Celestial $w_{1+\infty }$ Symmetries from Twistor Space
• Massless Scalars and Higher-Spin BMS in Any Dimension
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• Black Holes in Klein Space
• Soft Scalars and the Geometry of the Space of Celestial CFTs
• Deforming Soft Algebras for Gauge Theory
• Gauge independent kinematic algebra of self-dual Yang-Mills theory
• Four-point correlators of light-ray operators in CCFT
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• Celestial Supersymmetry
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• Multicollinear Singularities in Celestial CFT
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• Supersymmetric celestial OPEs and soft algebras from the ambitwistor string worldsheet
• Toward A Supersymmetric $w_{1+\infty }$ Symmetry in the Celestial Conformal Field Theory
• Lorentz Symmetry and IR Structure of The BFSS Matrix Model
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• Asymptotic Higher Spin Symmetries I: Covariant Wedge Algebra in Gravity
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• Deformed $w_{1+\infty }$ Algebras in the Celestial CFT
• Structure of deformed $w_{1+\infty }$ symmetry and topological generalization in Celestial CFT
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• Radiation in Fluid/Gravity and the Flat Limit
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• Multiparticle Contributions to the Celestial OPE
• Celestial $s{w}_{1+\infty }$ algebra in Einstein-Yang-Mills theory
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• Asymptotic Higher Spin Symmetries II: Noether Realization in Gravity
• Loop corrections versus marginal deformation in celestial holography
• Asymptotic Higher Spin Symmetries IV: Einstein-Yang-Mills Theory
• Non-abelian soft radiation data for a celestial theory
• A Celestial Description of Planar Super-Yang-Mills Theory
• Double-soft limit and celestial shadow OPE from charge bracket