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Celestial Operator Product Expansions and ${\rm w}_{1+\infty}$ Symmetry for All Spins
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abstract
The operator product expansion of massless celestial primary operators of arbitrary spin is investigated. Poincar\'e 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 ${\rm w}_{1+\infty}$. 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 ${\rm w}_{1+\infty}$ 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.
Forward citations
Cited by 7 Pith papers
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Light-Front approach to $4d$ massless Higher-Spin interactions
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S-algebra in Gauge Theory: Twistor, Spacetime and Holographic Perspectives
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Celestial OPE associativity, the Jacobi identity of a vertex-derived gauge algebra, vanishing four-point amplitudes, and the light-cone holomorphic constraint are shown to be the same consistency condition, solved for...
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Multi-Particle Contributions to the Celestial Algebra in the ${\cal N}=8$ Supergravity
Multi-particle OPEs of single-particle celestial operators with two-particle operators in N=8 supergravity yield ninety-five (anti)commutators of the soft current algebra plus amplitude relations.
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